Question

write the coordinates of the vertices after a reflection over the line x = -6.

Explanation:

Step1: Find the distance between each x - coordinate and the line \(x = - 6\)

For a point \((x,y)\) reflected over the line \(x = a\), the formula for the new \(x\) - coordinate is \(x'=2a - x\), and the \(y\) - coordinate remains the same \(y'=y\).
Let's first find the coordinates of \(P\) and \(Q\) from the graph. Assume \(P(-7,-8)\) and \(Q(-6,-3)\).
For point \(P(-7,-8)\):
The distance between \(x=-7\) and \(x = - 6\) is \(d=\vert-7-(-6)\vert=\vert-7 + 6\vert = 1\).
Using the formula \(x'=2\times(-6)-(-7)\)

Step2: Calculate the new x - coordinate for \(P\)

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Since \(y\) - coordinate remains the same (\(y=-8\)), the new coordinate of \(P\) is \(P'(-5,-8)\)
For point \(Q(-6,-3)\):
Using the formula \(x'=2\times(-6)-(-6)\)

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Since \(y\) - coordinate remains the same (\(y = - 3\)), the new coordinate of \(Q\) is \(Q'(-6,-3)\)
For point \(R(-10,-9)\) (assuming \(R\) is the third vertex):
Using the formula \(x'=2\times(-6)-(-10)\)

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Since \(y\) - coordinate remains the same (\(y=-9\)), the new coordinate of \(R\) is \(R'(-2,-9)\)

Answer:

\(P'(-5,-8)\), \(Q'(-6,-3)\), \(R'(-2,-9)\)