Question

10 the coordinates of △bcd and its image after a transformation are given below. identify the transformation. △bcd: b(1, -2), c(7, -6), d(3, -8) △bcd: b(-1, 2), c(-7, 6), d(-3, 8) a) reflection in the x - axis show off b) reflection in the y - axis get on the news c) 90° counterclockwise rotation win a bet d) 180° rotation get out of homework e) 270° counterclockwise rotation make people laugh *all rotations are about the origin.

Explanation:

Step1: Recall transformation rules

For a point $(x,y)$ reflected in the x - axis, the new point is $(x, - y)$. For reflection in the y - axis, the new point is $(-x,y)$. For a 90° counter - clockwise rotation about the origin, the new point of $(x,y)$ is $(-y,x)$. For a 180° rotation about the origin, the new point of $(x,y)$ is $(-x,-y)$. For a 270° counter - clockwise rotation about the origin, the new point of $(x,y)$ is $(y, - x)$.

Step2: Analyze given points

For point $B(1,-2)$ and $B'(-1,2)$, $x$ changes sign and $y$ changes sign. For point $C(7,-6)$ and $C'(-7,6)$, $x$ changes sign and $y$ changes sign. For point $D(3,-8)$ and $D'(-3,8)$, $x$ changes sign and $y$ changes sign. This follows the rule of a 180° rotation about the origin.

Answer:

D. 180° rotation