Question

triangle pqr is reflected across the line y = -2. the coordinates of the vertices of the image of △pqr are p(-4, -9), q(-2, -7), and r(5, -8). what are the coordinates of q?
a (6, 3)
b (-4, 3)
c (-2, 3)
d (-2, -7)

Explanation:

Step1: Recall reflection rule for y - coordinate

When reflecting a point $(x,y)$ across the line $y = k$, the formula for the new $y$ - coordinate is $y'=2k - y$. Here $k=-2$ and for point $Q'(-2,-7)$ where $x$ - coordinate remains the same in reflection across a horizontal line. Let the $y$ - coordinate of $Q$ be $y$.

Step2: Apply the formula

We know that $-7 = 2\times(-2)-y$. First, simplify the right - hand side: $2\times(-2)=-4$. So the equation becomes $-7=-4 - y$.

Step3: Solve for y

Add $y$ to both sides: $-7 + y=-4$. Then add 7 to both sides: $y=-4 + 7=3$. The $x$ - coordinate of $Q$ is the same as that of $Q'$ which is $x=-2$. So the coordinates of $Q$ are $(-2,3)$.

Answer:

C. (-2, 3)