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

When a point \((x,y)\) is reflected over the vertical line \(x = a\), the \(y\)-coordinate remains the same, and the \(x\)-coordinate satisfies the midpoint formula: \(\frac{x + x'}{2}=a\), where \((x',y')\) is the image of \((x,y)\). Here, \(a=-3\), and we know \(Q'\) has coordinates \((2,4)\). Let \(Q=(x,4)\) (since \(y\)-coordinate doesn't change).

Step2: Apply midpoint formula

Using the midpoint formula for the \(x\)-coordinate: \(\frac{x + 2}{2}=-3\). Multiply both sides by 2: \(x + 2=-6\). Subtract 2 from both sides: \(x=-6 - 2=-8\). So the coordinates of \(Q\) are \((-8,4)\).

Answer:

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