Question 1

In the accompanying diagram of right triangle $ABC$, altitude $\overline {BD}$ is drawn to hypotenuse $\overline{AC}$.

Which statement must always be true?

Accepted Answer

$\frac{AD}{AB}=\frac{AB}{AC}$

Answer

$\frac{AD}{AB}=\frac{BC}{AC}$

Answer

$\frac{AB}{BC}=\frac{BD}{AC}$

Answer

$\frac{BD}{BC}=\frac{AB}{AD}$

Question 2

Triangle $RJM$ has an area of 6 and a perimeter of 12. If the triangle is dilated by a scale factor of 3 centered at the origin, what are the area and perimeter of its image, triangle $R'J'M'?$

Accepted Answer

area of 54 and perimeter of 36

Answer

area of 18 and perimeter of 36

Answer

area of 9 and perimeter of 15

Answer

area of 54 and perimeter of 108

Question 3

After a dilation with center (0,0), the image of $\overline{DB}$ is $\overline{D'B'}$. If $DB=4.5$ and  $D'B'=18$, the scale factor of this dilation is

Accepted Answer

4

Answer

5

Answer

$\frac1{4}$

Answer

$\frac1{5}$

Question 4

On the set of axes below, $\Delta ABC$ has vertices at $A(-2,0), B(2,-4), C(4,2)$, and $\Delta DEF$ has vertices at $D(4,0), E(-4,8), F(-8,-4)$.
Which sequence of transformations will map $\Delta ABC$  onto $\Delta DEF$?

Accepted Answer

a dilation of  $\Delta ABC$  by a scale factor of 2 centered at the origin, followed by a rotation of $180\degree$ about the origin

Answer

a dilation of  $\Delta ABC$  by a scale factor of 2 centered at point $A$

Answer

a dilation of  $\Delta ABC$  by a scale factor of $\frac1{2}$ centered at point $A$

Answer

a dilation of  $\Delta ABC$  by a scale factor of $\frac1{2}$ centered at the origin, followed by a rotation of $180\degree$ about the origin

Question 5

What is an equation of the image of the line $y=\frac{3}{2}x-4$ after a dilation of a scale factor of $\frac{3}{4}$ centered at the origin?

Accepted Answer

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

Answer

$y=\frac{9}{8}x-4$

Answer

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

Answer

$y=\frac{9}{8}x-3$

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