Question

△ABC is reflected to form​​ ​ △A′B′C′ ​.

The vertices of △ABC are A(−7, 1) , B(−5, −3) , and C(−3, 2) . The vertices of △A′B′C′ are A′(−7, −1) , B′(−5, 3) , and C′(−3, −2) .

Which reflection results in the transformation of ​ △ABC ​​ to ​ △A′B′C′ ​​?

A)reflection across the x-axis

B) reflection across the y-axis

C)reflection across y = x

D)reflection across y=−x

Answer 1

C, Reflection across Y = X

Answer 2

The correct option is A.

Explanation:

The vertices of △ABC are A(−7, 1) , B(−5, −3) , and C(−3, 2) . The vertices of △A′B′C′ are A′(−7, −1) , B′(−5, 3) , and C′(−3, −2) .

The relation between coordinates of preimage and image is defined as

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

Sign of y-coordinate changes but x-coordinate remains the same. It is possible it the figure is reflection across the x-axis.

Therefore the correct option is A.