Question

triangle def with vertices d(-6, -1), e(-3, -2), and f(-5, -7): (a) reflection: in the x - axis (b) rotation: 180° d( ) e( ) f( )

Explanation:

Step1: Apply reflection rule for x - axis

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

Step2: Apply rotation rule for 180°

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

Answer:

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