Question

1. rhombus pqrs with vertices p(-8, 6), q(-4, 8), r(0, 6), and s(-4, 4): y = 2 p(__ ) q( ) r( ) s( __)

Explanation:

Step1: Recall reflection formula

For a point $(x,y)$ reflected over the horizontal line $y = k$, the formula is $(x,2k - y)$. Here $k = 2$.

Step2: Find $P'$

For point $P(-8,6)$, using the formula: $x=-8$, $y = 6$, then $y'=2\times2 - 6=- 2$. So $P'(-8,-2)$.

Step3: Find $Q'$

For point $Q(-4,8)$, $x=-4$, $y = 8$, then $y'=2\times2 - 8=-4$. So $Q'(-4,-4)$.

Step4: Find $R'$

For point $R(0,6)$, $x = 0$, $y = 6$, then $y'=2\times2 - 6=-2$. So $R'(0,-2)$.

Step5: Find $S'$

For point $S(-4,4)$, $x=-4$, $y = 4$, then $y'=2\times2 - 4=0$. So $S'(-4,0)$.

Answer:

$P'(-8,-2)$
$Q'(-4,-4)$
$R'(0,-2)$
$S'(-4,0)$