The coordinate of triangle after the rotation and reflection is A"(-4,2), B"(-4,4) and C"(-2,4). Hence the triangle 1 shows the final image.
How to rotate and reflect the figure?
Rotation of an object is rotating it about a fixed point without changing its shape and size.
Reflecting of an object is flipping it across a line without changing its shape and size.
Given information-
The [tex]\Delta ABC[/tex] is given in the problem.
The rule ry-axis • RO, 90°(x, y) is applied to ΔABC.
The rotation will change the y axis with the above rule.
- The coordinate of A is [tex](2,-4)[/tex] Thus change the coordinate of the A as,
[tex]A'=A(-y,x)\\A'=(4,2)[/tex]
- The coordinate of B is [tex](4,-4)[/tex] Thus change the coordinate of the B as,
[tex]B'=B(-y,x)\\B'=(4,4)[/tex]
- The coordinate of C is [tex](4,-2)[/tex] Thus change the coordinate of the C as,
[tex]C'=C(-y,x)\\C'=(2,4)[/tex]
The reflection across the y-axis with the above rule.
- The coordinate of A' is [tex](4,2)[/tex] Thus change the coordinate of the A as,
[tex]A"=A'(-x,y)\\A"=(-4,2)[/tex]
- The coordinate of B' is [tex](4,4)[/tex] Thus change the coordinate of the B as,
[tex]B"=B'(-x,y)\\B"=(-4,4)[/tex]
- The coordinate of C' is [tex](2,4)[/tex] Thus change the coordinate of the C as,
[tex]C"=C'(-x,y)\\C"=(-2,4)[/tex]
Thus the coordinate of triangle after the rotation and reflection is A"(-4,2), B"(-4,4) and C"(-2,4). Hence the triangle 1 shows the final image.
Learn more about the rotation and reflection of figure here;
https://brainly.com/question/17174293
