Question

triangle pqr is reflected over a vertical line of reflection to create trianglepqr. what are the coordinates of point r? p (-8,9) q (-12,7) r (-11,1) p(-6,9)

Explanation:

Step1: Find the line of reflection

The $x$ - coordinate of $P(-8,9)$ changes to $x=-6$ in $P'(-6,9)$. The mid - point of the line segment joining $P$ and $P'$ gives the line of reflection. The mid - point formula for two points $(x_1,y_1)$ and $(x_2,y_2)$ is $(\frac{x_1 + x_2}{2},\frac{y_1 + y_2}{2})$. For $P(-8,9)$ and $P'(-6,9)$, the $x$ - coordinate of the mid - point is $\frac{-8+( - 6)}{2}=\frac{-8 - 6}{2}=-7$. So the line of reflection is $x = - 7$.

Step2: Reflect point $R$

The $x$ - coordinate of point $R$ is $x_R=-11$. The distance between $x_R=-11$ and the line of reflection $x = - 7$ is $d=-7-(-11)=4$. The $x$ - coordinate of $R'$ is $-7 + 4=-3$. The $y$ - coordinate of a point does not change in a vertical line reflection. Since the $y$ - coordinate of $R$ is $y_R = 1$, the $y$ - coordinate of $R'$ is also $1$.

Answer:

$(-3,1)$