Question

Plz help i can't figure this out for the life of me and it's due tmr

Answer 1

D

Explanation:

The diagram shows the rectangle with vertices at A(3,4), B(3,7), C(4,7) and D(4,4).

1. Rotate rectangle ABCD by 180° about the point (3,4) (vertex A). This rotation has the rule:

`(x,y)\rightarrow (6-x,8-y)`

So, the image points have the coordinates A'(3,4), B'(3,1), C'(2,1) and D'(2,4)

2. Dilate by a scale factor of 2 with the center of dilation at origin. This dilation has the rule:

`(x,y)\rightarrow (2x,2y)`

So, the image points have the coordinates A''(6,8), B''(6,2), C''(4,2) and D''(4,8)

3. Reflect it over the y-axis. This reflection has the rule:

`(x,y)\rightarrow (-x,y)`

So, the image points have the coordinates A'''(-6,8), B'''(-6,2), C'''(-4,2) and D'''(-4,8) that are exactly the coordinates of the second rectangle shown.

Thus, correct option is option D.