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′ ​​?

Answer 1

the vertices of the preimage and final image are as follows
A(−7, 1) ---> A′(−7, −1)
B(−5, −3) ---> B′(−5, 3)
C(−3, 2) ---> C′(−3, −2)
it can be noted that whilst the x coordinates remain the same in the final image, y coordinate values, the sign changes.
eg: A (x = -7) and A' (x = -7)
therefore x coordinates haven't changed the value nor sign
A (y = 1) and A' (y = -1)
y coordinates have been multiplied by -1 hence changing the sign.
the reflection goes as (x,y) = (x,-y)
this is a reflection over the x axis.