Question

fill in the blank 6 points
the vertices of a triangle are p(-3, 8), q(-4, -4), and r(1, 1). graph and name the vertices of the image reflected over x = 2.
los vértices de un triángulo son p(-3, 8), q(-4, -4), y r(1, 1). grafica y nombra los vértices de la imagen reflejados sobre x = 2.

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. Here $a = 2$.

Step2: Find the image of point P

For point $P(-3,8)$, the new $x$ - coordinate is $2\times2-(-3)=4 + 3=7$, and the $y$ - coordinate remains $8$. So the image of $P$ is $P'(7,8)$.

Step3: Find the image of point Q

For point $Q(-4,-4)$, the new $x$ - coordinate is $2\times2-(-4)=4 + 4 = 8$, and the $y$ - coordinate remains $-4$. So the image of $Q$ is $Q'(8,-4)$.

Step4: Find the image of point R

For point $R(1,1)$, the new $x$ - coordinate is $2\times2 - 1=4 - 1=3$, and the $y$ - coordinate remains $1$. So the image of $R$ is $R'(3,1)$.

Answer:

The vertices of the reflected triangle are $P'(7,8)$, $Q'(8,-4)$, and $R'(3,1)$.