Question

△ABC is reflected to form​​ ​ △A′B′C′ ​. The vertices of △ABC are A(-1, 3) , B(2, 4) , and C(-5, 6) . The vertices of △A′B′C′ are A′(3, −1) , B′(4, 2) , and C′(6, −5) . 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

Explanation:

The given transfomation is

`A(-1,3) \implies A'(3,-1)\\B(2,4) \implies B'(4,2)\\C(-5,6) \implies C'(6,-5)`

Notice that the rule of the given transformation is

`(x,y) \implies (y,x)`

That is, the coordinates were change of position, like an inverse.

According to transformation rules, this represents a reflection across the line
`y=x`.

Therefore, the right answer is C.

Answer 2

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

→→Vertices of △ABC are A(-1, 3) , B(2, 4) , and C(-5, 6) and the vertices of △A′B′C′ are A′(3, −1) , B′(4, 2) , and C′(6, −5) .

Drawing the two images of ΔABC and ΔA'B'C'on two Dimensional Coordinate Plane

When, reflection takes place,the two, Image, and Pre-Image are Congruent, that is neither the shape nor the Size changes only translation of the shape takes place on the coordinate plane.

Option C: → Reflection across y = x.