Question

give the coordinates of the new image. 5. triangle pqr with vertices p(-2, 3), q(2, 4), and r(1, -1): x = -3

Explanation:

Step1: Recall reflection formula

For a point $(x,y)$ reflected over the vertical line $x = a$, the new $x$-coordinate is $2a - x$ and the $y$-coordinate remains the same.

Step2: Find $P'$

For point $P(-2,3)$ reflected over $x=-3$, new $x = 2\times(-3)-(-2)=-6 + 2=-4$, $y = 3$. So $P'(-4,3)$.

Step3: Find $Q'$

For point $Q(2,4)$ reflected over $x = - 3$, new $x=2\times(-3)-2=-6 - 2=-8$, $y = 4$. So $Q'(-8,4)$.

Step4: Find $R'$

For point $R(1,-1)$ reflected over $x=-3$, new $x=2\times(-3)-1=-6 - 1=-7$, $y=-1$. So $R'(-7,-1)$.

Answer:

$P'(-4,3)$
$Q'(-8,4)$
$R'(-7,-1)$