Question

directions: graph and label each figure and its image. all rotations are about the origin. 9. triangle def with vertices d(-6, -1), e(-3, -2), and f(-5, -7): (a) reflection: in the x - axis (b) rotation: 180°

Explanation:

Step1: Find reflection in x - axis

The rule for reflecting a point $(x,y)$ in the $x$-axis is $(x,-y)$.
For point $D(-6,-1)$, its reflection $D'$ is $(-6,1)$.
For point $E(-3,-2)$, its reflection $E'$ is $(-3,2)$.
For point $F(-5,-7)$, its reflection $F'$ is $(-5,7)$.

Step2: Find 180 - degree rotation

The rule for rotating a point $(x,y)$ 180 degrees about the origin is $(-x,-y)$.
For point $D(-6,-1)$, its rotated image $D''$ is $(6,1)$.
For point $E(-3,-2)$, its rotated image $E''$ is $(3,2)$.
For point $F(-5,-7)$, its rotated image $F''$ is $(5,7)$.

Answer:

(a) $D'(-6,1), E'(-3,2), F'(-5,7)$
(b) $D''(6,1), E''(3,2), F''(5,7)$