Question

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

Explanation:

Step1: Use the reflection formula for \(x\) - coordinate

The formula for reflecting a point \((x,y)\) across the line \(x = a\) is \((2a - x,y)\). Here \(a=-3\), and we know the image point \(Q'(x',y')=(2,4)\). Let the original point \(Q=(x,y)\). Using the formula \(x'=2a - x\), substituting \(x' = 2\) and \(a=-3\) gives \(2=2\times(-3)-x\).

Step2: Solve for \(x\)

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The \(y\) - coordinate remains the same during reflection across a vertical line \(x = a\). So \(y = 4\)

Answer:

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