Question 1

What is the equation of a line that is parallel to the line whose equation is y = x + 2?

Accepted Answer

y − x = −1

Answer

2x + y = −2

Answer

y − 2x = 3

Answer

x + y = 5

Question 2

What is the slope of a line perpendicular to the line whose equation is y = −$\frac{2}{3}$x − 5?

Accepted Answer

$\frac{3}{2}$

Answer

-$\frac{3}{2}$

Answer

$\frac{2}{3}$

Answer

-$\frac{2}{3}$

Question 3

What is an equation of the line that passes through the point (6,−5) and is parallel to the line whose equation is 2x − 3y = 11?

Accepted Answer

y = $\frac{2}{3}$(x - 6) - 5

Answer

y = -$\frac{3}{2}$(x - 6) - 5

Answer

y = -$\frac{2}{3}$(x - 6) - 5

Answer

y = $\frac{3}{2}$(x - 6) - 5

Question 4

The lines represented by the equations y + $\frac{1}{2}$x = 4 and 3x + 6y = 12 are

Accepted Answer

parallel

Answer

the same line

Answer

neither parallel nor perpendicular

Answer

perpendicular

Question 5

What is the slope of a line perpendicular to the line whose equation is 2y = −6x + 8?

Accepted Answer

$\frac{1}{3}$

Answer

-3

Answer

-6

Answer

$\frac{1}{6}$

Question 6

The equation of a circle is x$^{2}$ + (y − 7)$^{2}$ = 16. What are the center and radius of the circle?

Accepted Answer

(0,7) and 4

Answer

(0,7) and 16

Answer

(0,-7) and 16

Answer

(0,-7) and 4

Question 7

Which equation represents circle K shown in the graph?

Accepted Answer

(x + 5)$^{2}$ + (y - 1)$^{2}$ = 9

Answer

(x - 5)$^{2}$ + (y + 1)$^{2}$ = 9

Answer

(x + 5)$^{2}$ + (y - 1)$^{2}$ = 3

Answer

(x - 5)$^{2}$ + (y + 1)$^{2}$ = 3

Question 8

What are the center and the radius of the circle whose equation is (x - 3)$^{2}$ + (y + 3)$^{2}$ = 36

Accepted Answer

(3, -3) and 6

Answer

(-3, 3) and 6

Answer

(3, -3) and 36

Answer

(-3, 3) and 36

Question 9

What is an equation of the circle with a radius of 5 and center at (1,−4)?

Accepted Answer

(x - 1)$^{2}$ + (y + 4)$^{2}$ = 25

Answer

(x + 1)$^{2}$ + (y - 4)$^{2}$ = 5

Answer

(x - 1)$^{2}$ + (y + 4)$^{2}$ = 5

Answer

(x + 1)$^{2}$ + (y - 4)$^{2}$ = 25

Question 10

Which equation represents the line parallel to the line whose equation is 4x + 2y = 14 and passing through the point (2,2)?

Accepted Answer

y = −2x + 6

Answer

y = $\frac{1}{2}$x

Answer

y = −2x

Answer

y = $\frac{1}{2}$x + 1

Question 11

Which equation represents the perpendicular bisector of AB whose endpoints are A(8,2) and B(0,6)?

Accepted Answer

y = 2x − 4

Answer

y = 2x − 12

Answer

y = -$\frac{1}{2}$x + 6

Answer

y = -$\frac{1}{2}$x + 2

Question 12

The equation of a circle with its center at (-3,5) and a radius of 4 is

Accepted Answer

(x + 3)$^{2}$ + (y - 5)$^{2}$ = 16

Answer

(x - 3)$^{2}$ + (y + 5)$^{2}$ = 16

Answer

(x + 3)$^{2}$ + (y - 5)$^{2}$ = 4

Answer

(x - 3)$^{2}$ + (y + 5)$^{2}$ = 4

Question 13

What is an equation of the circle shown in the graph below?

Accepted Answer

(x + 3)$^{2}$ + (y + 4)$^{2}$ = 25

Answer

(x + 3)$^{2}$ + (y + 4)$^{2}$ = 10

Answer

(x - 3)$^{2}$ + (y - 4)$^{2}$ = 25

Answer

(x - 3)$^{2}$ + (y - 4)$^{2}$ = 10

Question 14

Which equation represents a line that is parallel to the line whose equation is y = $\frac{3}{2}$x + 3 and passes through the point (1,2)?

Accepted Answer

y = $\frac{3}{2}$x + $\frac{1}{2}$

Answer

y = $\frac{3}{2}$x - 2

Answer

y = -$\frac{2}{3}$x + $\frac{8}{3}$

Answer

y = $\frac{2}{3}$x + $\frac{4}{3}$

Question 15

Which equation represents the line that is perpendicular to 2y = x + 2 and passes through the point (4,3)?

Accepted Answer

y = -2x - 5

Answer

y = -2x + 11

Answer

y = $\frac{1}{2}$x - 5

Answer

y = $\frac{1}{2}$x + 1

Question 16

What is an equation of the circle with center (-5,4) and a radius of 7?

Accepted Answer

(x + 5)$^{2}$ + (y - 4)$^{2}$ = 49

Answer

(x - 5)$^{2}$ + (y + 4)$^{2}$ = 49

Answer

(x + 5)$^{2}$ + (y - 4)$^{2}$ = 14

Answer

(x - 5)$^{2}$ + (y + 4)$^{2}$ = 14

Question 17

Which is an equation of the graphed circle?

Accepted Answer

(x + 4)$^{2}$ + (y - 1)$^{2}$ = 9

Answer

(x - 4)$^{2}$ + (y + 1)$^{2}$ = 3

Answer

(x - 4)$^{2}$ + (y + 1)$^{2}$ = 9

Answer

(x + 4)$^{2}$ + (y - 1)$^{2}$ = 3

Question 18

The lines represented by the equations 3y + 6 = 2x and 2y - 3x = 6 are

Accepted Answer

intersecting but not perpendicular

Answer

parallel

Answer

perpendicular

Answer

the same line

Question 19

Which graph represents a circle whose equation is x$^{2}$ + (y - 2)$^{2}$ = 4

Accepted Answer

https://uploads.quizalize.com/114243f8-bacc-4183-a8f0-543905efe89a/question/0974b1bfd93082b84a95fcdca5d537b7b2c12986.png

Answer

https://uploads.quizalize.com/114243f8-bacc-4183-a8f0-543905efe89a/question/5c7c6879d9512abcca92a73c138b03faa59efba6.png

Answer

https://uploads.quizalize.com/114243f8-bacc-4183-a8f0-543905efe89a/question/d15fa020e9e3cc2b6dc7af25f34df0c275b26eb2.png

Answer

https://uploads.quizalize.com/114243f8-bacc-4183-a8f0-543905efe89a/question/dd4f4054b4d60201e936c9f0d95eccb105fd1fd2.png

Question 20

Triangle ABC has vertices with coordinates A(0,0), B(6,8), and C(8,4). Which equation represents the perpendicular bisector of BC?

Accepted Answer

y = $\frac{1}{2}$x + $\frac{5}{2}$

Answer

y = -$\frac{1}{2}$x + $\frac{19}{2}$

Answer

y = -2x + 4

Answer

y = 2x - 6

Question 21

A circle has the equation (x - 3)$^{2}$ + (y + 4)$^{2}$ = 10. The coordinates of the center of the circle and the length of the circle’s radius are

Accepted Answer

(-3, 4) and $\sqrt{10}$

Answer

(-3, 4) and 5

Answer

(3, -4) and 5

Answer

(3, -4) and $\sqrt{10}$

Question 22

What is an equation of the line that passes through (-9,12) and is perpendicular to the line whose equation is y = $\frac{1}{3}$x + 6?

Accepted Answer

y = -3x - 15

Answer

y = -3x + 27

Answer

y = $\frac{1}{3}$x - 13

Answer

y = $\frac{1}{3}$x + 15

Question 23

The equation of a circle is x$^{2}$ + y $^{2}$ + 6y = 7.  What are the coordinates of the center and the length of the radius of the circle?

Accepted Answer

(0, -3) and 4

Answer

(0, 3) and 4

Answer

(0, -3) and 16

Answer

(0, 3) and 16

Question 24

If x$^{2}$ + y $^{2}$ + 4x - 6y - 12 = 0 is the equation of a circle, the length of the radius is

Accepted Answer

5

Answer

25

Answer

16

Answer

4

Question 25

What are the coordinates of the center and length of the radius of the circle whose equation is x$^{2}$ + y $^{2}$ + 6x - 4y = 23

Accepted Answer

(-3, 2) and 6

Answer

(-3, 2) and 36

Answer

(3, -2) and 6

Answer

(3, -2) and 36

Question 26

Kevin’s work for deriving the equation of a circle is shown.  In which step did Kevin make an error?

Accepted Answer

Step 2

Answer

Step 4

Answer

Step 1

Answer

Step 3

Question 27

What are the coordinates of the center and the length of the radius of the circle whose equation is x$^{2}$ + y $^{2}$ - 6y + 1 = 0?

Accepted Answer

(0, 3) and 2$\sqrt{2}$

Answer

(0, -3) and 2$\sqrt{2}$

Answer

(0, 3) and $\sqrt{35}$

Answer

(0, -3) and $\sqrt{35}$

Question 28

What are the coordinates of the center and the length of the radius of the circle represented by the equation x$^{2}$ + y $^{2}$ - 4x + 8y + 11 = 0

Accepted Answer

(2, -4) and 3

Answer

(-2, 4) and 3

Answer

(2, -4) and 9

Answer

(-2, 4) and 9

Question 29

The equation of a circle is x$^{2}$ + y $^{2}$ - 12y + 20 = 0. What are the coordinates of the center and the length of the radius of the circle?

Accepted Answer

(0, 6) and 4

Answer

(0, -6) and 16

Answer

(0, 6) and 16

Answer

(0, -6) and 4

Question 30

The equation of a circle is x$^{2}$ + y $^{2}$ - 6x + 2y = 6. What are the coordinates of the center and the length of the radius of the circle?

Accepted Answer

(3, -1) and 4

Answer

(-3, 1) and 16

Answer

(3, -1) and 16

Answer

(-3, 1) and 4

Question 31

What is an equation of circle O shown in the graph below?

Accepted Answer

x$^{2}$ + y $^{2}$ - 10x - 4y = -13

Answer

x$^{2}$ + y $^{2}$ + 10x + 4y = -25

Answer

x$^{2}$ + y $^{2}$ - 10x - 4y = -25

Answer

x$^{2}$ + y $^{2}$ + 10x + 4y = -13

Question 32

An equation of circle O is x$^{2}$ + y $^{2}$ + 4x - 8y = -16.  The statement that best describes circle O is the

Accepted Answer

center is (-2, 4) and it is tangent to the y-axis

Answer

center is (-2, 4) and it is tangent to the x-axis

Answer

center is (2, -4) and it is tangent to the x-axis

Answer

center is (2, -4) and it is tangent to the y-axis

Question 33

What is an equation of a circle whose center is (1,4) and diameter is 10?

Accepted Answer

x$^{2}$ + y $^{2}$ - 2x - 8y = 8

Answer

x$^{2}$ + y $^{2}$ - 2x - 8y = 83

Answer

x$^{2}$ + y $^{2}$ + 2x + 8y = 8

Answer

x$^{2}$ + y $^{2}$ + 2x + 8y = 83

Question 34

The equation of a circle is x$^{2}$ + y $^{2}$ + 8x - 12y = 144.  What are the coordinates of the center and the length of the radius of the circle?

Accepted Answer

(-4, 6) and 14

Answer

(-4, 6) and 12

Answer

(4, -6) and 12

Answer

(4, -6) and 14

Question 35

What is an equation of a circle whose center is at (2, 4) and is tangent to the line x = -2?

Accepted Answer

(x - 2)$^{2}$ + (y + 4)$^{2}$ = 16

Answer

(x - 2)$^{2}$ + (y + 4)$^{2}$ = 4

Answer

(x + 2)$^{2}$ + (y - 4)$^{2}$ = 4

Answer

(x + 2)$^{2}$ + (y - 4)$^{2}$ = 16

Question 36

Which equation represents a line that is perpendicular to the line represented by 2x - y = 7?

Accepted Answer

y = -$\frac{1}{2}$x + 6

Answer

y = 2x + 6

Answer

y = $\frac{1}{2}$x + 6

Answer

y = -2x + 6

Question 37

The coordinates of the endpoints of AB are A(-6, -5) and B(4,0). Point P is on AB. Determine and state the coordinates of point P, such that AP:PB is 2:3.  [Be sure to write your answer in the form (x, y)]

Accepted Answer

(-2, -3)

Question 38

Point Q is on MN such that MQ:QN = 2:3. If M has coordinates (3,5) and N has coordinates (8, -5), the coordinates of Q are

Accepted Answer

(5, 1)

Answer

(6, -1)

Answer

(5, 0)

Answer

(6, 0)

Question 39

Given MN shown, with M(-6,1) and N(3,-5), what is an
equation of the line that passes through point P(6,1) and is parallel to MN?

Accepted Answer

y = -$\frac{2}{3}$x + 5

Answer

y = $\frac{3}{2}$x - 8

Answer

y = -$\frac{2}{3}$x - 3

Answer

y = $\frac{3}{2}$x + 7

Question 40

The endpoints of DEF are D(1,4) and F(16,14). Determine and state the coordinates of point E, if DE:EF = 2:3.  [Be sure to write your answer in the form (x, y)]

Accepted Answer

(7,8)

Question 41

An equation of a line perpendicular to the line represented by the equation y= -$\frac{1}{2}$x - 5 and passing through (6, 4) is

Accepted Answer

y = 2x - 16

Answer

y= -$\frac{1}{2}$x + 4

Answer

y= -$\frac{1}{2}$x - 1

Answer

y = 2x + 14

Question 42

Directed line segment PT has endpoints whose coordinates are P(-2,1) and T(4,7). Determine the coordinates of point J, on PT, that divides the segment in the ratio 2 to 1.  [Be sure to write your answer in the form (x, y)]

Accepted Answer

(2, 5)

Question 43

Line segment NY has endpoints N(-11,5) and Y(5, -7). What is the equation of the perpendicular bisector of NY ?

Accepted Answer

y + 1 = $\frac{4}{3}$ (x + 3)

Answer

y - 6 = $\frac{4}{3}$ (x - 8)

Answer

y + 1 = -$\frac{3}{4}$ (x + 3)

Answer

y - 6 = -$\frac{3}{4}$ (x - 8)

Question 44

Point P is on segment AB such that AP:PB is 4:5. If A has coordinates (4,2), and B has coordinates (22,2), determine and state the coordinates of P.  [Be sure to write your answer in the form (x, y)]

Accepted Answer

(12, 2)

Question 45

The diagonals of rhombus TEAM intersect at P(2,1). If the equation of the line that contains diagonal TA is y = -x + 3, what is the equation of a line that contains diagonal EM ?

Accepted Answer

y = x - 1

Answer

y = -x - 3

Answer

y = -x - 1

Answer

y = x - 3

Question 46

Point P is on the directed line segment from point X(-6, -2) to point Y(6,7) and divides the segment in the ratio 1:5. What are the coordinates of point P?

Accepted Answer

(-4, -$\frac{1}{2}$)

Answer

(-$\frac{1}{2}$, -4)

Answer

(4, 5$\frac{1}{2}$)

Answer

(-4$\frac{1}{2}$, 0)

Question 47

Line segment RW has endpoints R(-4,5) and W(6,20). Point P is on RW such that RP:PW is 2:3. What are the coordinates of point P?

Accepted Answer

(0, 11)

Answer

(10, 2)

Answer

(2, 9)

Answer

(2, 14)

Question 48

What is an equation of a line that is perpendicular to the line whose equation is 2y = 3x - 10 and passes through (-6,1)?

Accepted Answer

y = -$\frac{2}{3}$x - 3

Answer

y = $\frac{2}{3}$x + 10

Answer

y = -$\frac{2}{3}$x - 5

Answer

y = $\frac{2}{3}$x + 1

Question 49

The coordinates of the endpoints of AB are A(-8, -2) and B(16,6). Point P is on AB. What are the coordinates of point P, such that AP:PB is 3:5?

Accepted Answer

(1, 1)

Answer

(9.6, 3.6)

Answer

(6.4, 2.8)

Answer

(7, 3)

Question 50

What is an equation of the perpendicular bisector of the line segment shown in the diagram?

Accepted Answer

2y - x = 0

Answer

2y + x = 0

Answer

y - 2x = 0

Answer

y + 2x = 0

Question 51

In the diagram, AC has endpoints with coordinates A(-5,2) and C(4, -10).  If B is a point on AC and AB:BC = 1:2, what are the coordinates of B?

Accepted Answer

(-2, -2)

Answer

(0, -$\frac{14}{3}$)

Answer

(-$\frac{1}{2}$, 4)

Answer

(1, -6)

Question 52

What is an equation of a line which passes through (6,9) and is perpendicular to the line whose equation is 4x - 6y = 15?

Accepted Answer

y - 9 = -$\frac{3}{2}$(x - 6)

Answer

y - 9 = -$\frac{2}{3}$(x - 6)

Answer

y + 9 = -$\frac{2}{3}$(x + 6)

Answer

y + 9 = -$\frac{3}{2}$(x + 6)

Question 53

What is an equation of the line that passes through the point (6,8) and is perpendicular to a line with equation y= $\frac{3}{2}$x + 5?

Accepted Answer

y - 8 = -$\frac{2}{3}$(x - 6)

Answer

y + 8 = $\frac{3}{2}$(x + 6)

Answer

y - 8 = $\frac{3}{2}$(x - 6)

Answer

y + 8 = -$\frac{2}{3}$(x + 6)

Question 54

Directed line segment DE has endpoints D(-4, -2) and E(1,8). Point F divides DE such that DF:FE is 2:3. What are the coordinates of F?

Accepted Answer

(-2, 2)

Answer

(-1, 4)

Answer

(2, 4)

Answer

(-3, 0)

Question 55

Which equation represents a line that is perpendicular to the line represented by y = $\frac{2}{3}$x + 1?

Accepted Answer

3x + 2y = 12

Answer

y = -$\frac{2}{3}$x + 4

Answer

y = $\frac{3}{2}$x + 2

Answer

3x - 2y = 12

Question 56

The coordinates of the endpoints of directed line segment ABC are A(-8, 7) and C(7, -13). If AB:BC = 3:2, the coordinates of B are

Accepted Answer

(1, -5)

Answer

(-2, -1)

Answer

(3, -6)

Answer

(-3, 0)

Question 57

Point M divides AB so that AM:MB = 1:2. If A has coordinates (-1, -3) and B has coordinates (8,9), the coordinates of M are

Accepted Answer

(2, 1)

Answer

($\frac{5}{3}$, 0)

Answer

($\frac{23}{3}$, 8)

Answer

(5, 5)

Question 58

Which equation represents a line parallel to the line whose equation is  -2x + 3y = -4 and passes through the point (1,3)?

Accepted Answer

y - 3 = $\frac{2}{3}$(x - 1)

Answer

y + 3 = -$\frac{3}{2}$(x + 1)

Answer

y - 3 = -$\frac{3}{2}$(x - 1)

Answer

y + 3 = $\frac{2}{3}$(x + 1)

Question 59

What are the coordinates of point C on the directed segment from A(-8,4) to B(10,-2) that partitions the segment such that AC:CB is 2:1?

Accepted Answer

(4, 0)

Answer

(2, -2)

Answer

(1, 1)

Answer

(-2, 2)

Question 60

The endpoints of directed line segment PQ have coordinates of P(-7, -5) and Q(5,3). What are the coordinates of point A, on PQ, that divide PQ into a ratio of 1:3?

Accepted Answer

(-4, -3)

Answer

(-1, -1)

Answer

(3, 2)

Answer

(2, 1)

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