Question

pq is reflected across the line x = -3. the coordinates of the endpoints of the image of pq are p’(5,2) and q’(2,4). what are the coordinates of q? a (1,4) b (-3,4) c (5,4) d (-8,4)

Explanation:

Step1: Recall reflection over vertical line

For a reflection over the vertical line \( x = a \), the midpoint between a point \( (x,y) \) and its image \( (x',y') \) lies on \( x = a \). The formula for the midpoint's \( x \)-coordinate is \( \frac{x + x'}{2}=a \). Here, \( a=-3 \), and we know \( Q'=(2,4) \), let \( Q=(x,4) \) (since the \( y \)-coordinate remains the same in vertical reflection).

Step2: Apply midpoint formula

Using \( \frac{x + 2}{2}=-3 \). Multiply both sides by 2: \( x + 2=-6 \). Subtract 2: \( x=-6 - 2=-8 \). So \( Q=(-8,4) \).

Answer:

D. \((-8, 4)\)