How can I find coordinates of the vertices of the figure after the given transformation?

Question

Reflection across y=2

J(1,3), U(0,5), R(1,5), C(3,2)

Answer 1

To reflect across y = 2, we need all these points' reflections to have the same x-coordinates, but their y-coordinates must be on the other side of the horizontal line y = 2 and equally far from it. For example, (3, 4), which is 2 units above y = 2, needs to become (3, 0), which is 2 units below y = 2.

 

So, do this:

 

J'(1, 2 + (2 - 3))

 

This finds the distance from the point to y = 2 by subtracting the point's y-coordinate from 2, then moves the point that far to the other side of y = 2 by adding 2.

 

J(1, 3) = J'(1, 2 + (2 - 3)) = J'(1, 2 - 1) = J'(1, 1)

U(0, 5) = U'(0, 2 + (2 - 5)) = U'(0, 2 - 3) = U'(0, -1)

R(1, 5) = R'(1, 2 + (2 - 5)) = R'(1, 2 - 3) = R'(1, -1)

C(3, 2) = C'(3, 2 + (2 - 2)) = C'(3, 2 + 0) = C'(3, 2)

 

 

Plot those points to make sure they haven't shifted horizontally, but have reflected across the line y = 2.