Question

triangle pqr has vertices at p(-3,3), q(-3,-2) and r(-1,-2). this triangle is transformed to make △pqr, as shown. if this transformation is a reflection, then what are the coordinates for point r? (1,-2) (5,3) (1,3) (5,-2)

Explanation:

Step1: Identify the axis of reflection

By observing the graph, the triangle is reflected over the line $x = 1$.

Step2: Use the reflection formula

The formula for reflecting a point $(x,y)$ over the line $x = a$ is $(2a - x,y)$. Here $a = 1$ and the point $R$ has coordinates $(-1,-2)$.
Substitute $x=-1$ and $a = 1$ into the formula: $2\times1-(-1)=2 + 1=3$, and $y=-2$ remains the same.

Answer:

A. $(1,-2)$