Question

Segment AB has endpoints A (-5, 7) and B (4, 4). The segment is reflected over the line y =4 to create endpoints A'B' and then rotated 90° CW to form points A"B". Find the location of A" and B".

Answer 1

A(-5,7)

B(4,4)

The segment is reflected over the line y =4

The line y=4 is a horizontal line, coordinate in x doesn't change after reflection.

To find coordinate y after reflection:

Find the distance of each point from y=4

Point A: (-5,7)$\lvert7-4\rvert=3$

As y=4 is below the point A, the point A' will have a coordinate y of: 4-3=1

Point A': (-5,1)

Point B: (4,4)$\lvert4-4\rvert=0$

As point B is on line y=4 the point B' will have a coordinate y of 4-0:4

Point B': (4,4)

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then rotated 90° CW:

Rule for a rotation 90º CW:

$P(x,y)\rightarrow P^{\prime}(y,-x)$

Then, you get the next coordinates for A'' and B'':

$\begin{gathered} A^{\prime}(-5,1)\rightarrow A^{\doubleprime}(1,5) \\ B^{\prime}(4,4)\rightarrow B^{\doubleprime}(4,-4) \end{gathered}$