Triangle ABC is shown in the coordinate plane. Triangle XYZ (not shown) is located in the coordinate plane with vertices at points X(9,0), Y(7,4), and Z(7,0).

Question

Which of the following transformations shows that triangle ABC is congruent to triangle XYZ?

A. Triangle ABC is translated 14 units to the right and 2 units down.

B. Triangle ABC is reflected over the x-axis and translated 2 units down.

C. Triangle ABC is reflected over the y-axis and translated 2 units down.

D. Triangle ABC is translated 14 units to the right and then a 90

Answer 1

Reflection over the x-axis switches the y-coordinate. (7,-4) reflects to (7,4), for example.

Reflection over the y-axis switches the x-coordinate. (-7,4) reflects to (7,4).

A 90° rotation switches (x,y) to (-y,x). (-4,7) rotates to (7,4).

Hopefully you can figure out what translating horizontally or vertically does.

Go!