Question

1. which sequence of transformations maps a rectangle from (1,2), (1,4), (3,4), and (3,2) to (-2,-4), (-2,-8), (-6,-8), and (-6,-4)?

a. dilation by scale factor of 2
b. dilation by scale factor of -2
c. translation by 2 units right
d. translation by 9 units left and 12 units down

Explanation:

Step1: Check dilation by scale factor of 2

If we dilate a point $(x,y)$ by a scale factor of 2, the new point is $(2x,2y)$. For example, if we take the point $(1,2)$, $(2\times1,2\times2)=(2,4)
eq(- 2,-4)$. So option a is incorrect.

Step2: Check dilation by scale factor of -2

If we dilate a point $(x,y)$ by a scale factor of -2, the new point is $(-2x,-2y)$. For the point $(1,2)$, $(-2\times1,-2\times2)=(-2,-4)$; for $(1,4)$, $(-2\times1,-2\times4)=(-2,-8)$; for $(3,4)$, $(-2\times3,-2\times4)=(-6,-8)$; for $(3,2)$, $(-2\times3,-2\times2)=(-6,-4)$. So option b is correct.

Step3: Check translation by 2 units right

A translation 2 units right of a point $(x,y)$ gives $(x + 2,y)$. For $(1,2)$, $(1+2,2)=(3,2)
eq(-2,-4)$. So option c is incorrect.

Step4: Check translation by 9 units left and 12 units down

A translation 9 units left and 12 units down of a point $(x,y)$ gives $(x-9,y - 12)$. For $(1,2)$, $(1-9,2 - 12)=(-8,-10)
eq(-2,-4)$. So option d is incorrect.

Answer:

B. dilation by scale factor of -2