Question

1. how would you transform a figure at (2,2), (4,2), (4,4), and (2,4) to (-3,-3), (-6,-3), (-6,-6), and (-3,-6)? a. reflection over the x - axis, then dilation by - 1 b. translation 1 unit left, then dilation by - 2 c. rotation 180 degrees, then dilation by 1.5 d. translation 1 unit left and 3 units down, then dilation by - 1.5

Explanation:

Step1: Analyze transformation rules

First, consider the general rules for translation, rotation, reflection and dilation. Let's check each option.

Step2: Check option a

Reflection over x - axis changes (x,y) to (x, - y). Then dilation by - 1 changes (x, - y) to (-x,y), which is not correct.

Step3: Check option b

Translation 1 unit left changes (x,y) to (x - 1,y). Then dilation by - 2 changes (x - 1,y) to (-2(x - 1),-2y). For example, for point (2,2), after translation it is (1,2), and after dilation it is (-2, - 4), not correct.

Step4: Check option c

Rotation 180 degrees changes (x,y) to (-x,-y). Dilation by 1.5 changes (-x,-y) to (-1.5x,-1.5y). For point (2,2), after rotation it is (-2,-2), and after dilation it is (-3,-3). For (4,2), after rotation (-4,-2) and after dilation (-6,-3), etc. This option is correct.

Step5: Check option d

Translation 1 unit left and 3 units down changes (x,y) to (x - 1,y - 3). Dilation by - 1.5 changes (x - 1,y - 3) to (-1.5(x - 1),-1.5(y - 3)), which is not correct.

Answer:

C. Rotation 180 degrees, then dilation by 1.5