Question

quadrilateral hdwm is shown on the coordinate grid. draw the quadrilateral that is the result of translation, 8 units right and 2 units down and then reflected across the y - axis.
pre - image translate 8 right, 2 down reflect across y - axis
h(-7,4) h(__,) h(,__)
d(-4,1) d(__,) d(,__)
w(-5,-3) w(__,) w(,__)
m(-9,-1) m(__,) m(,__)

Explanation:

Step1: Apply translation rule

For a translation of 8 units right and 2 units down, the rule for a point $(x,y)$ is $(x + 8,y - 2)$.
For point $H(-7,4)$: $H'=(-7 + 8,4 - 2)=(1,2)$
For point $D(-4,1)$: $D'=(-4 + 8,1 - 2)=(4,-1)$
For point $W(-5,-3)$: $W'=(-5 + 8,-3 - 2)=(3,-5)$
For point $M(-9,-1)$: $M'=(-9 + 8,-1 - 2)=(-1,-3)$

Step2: Apply reflection rule across y - axis

The rule for reflecting a point $(x,y)$ across the y - axis is $(-x,y)$.
For point $H'(1,2)$: $H''=(-1,2)$
For point $D'(4,-1)$: $D''=(-4,-1)$
For point $W'(3,-5)$: $W''=(-3,-5)$
For point $M'(-1,-3)$: $M''=(1,-3)$

Answer:

Pre - image	Translate 8 Right, 2 Down	Reflect across y - axis
$D(-4,1)$	$D'(4,-1)$	$D''(-4,-1)$
$W(-5,-3)$	$W'(3,-5)$	$W''(-3,-5)$
$M(-9,-1)$	$M'(-1,-3)$	$M''(1,-3)$