Question

1. triangle pqr with vertices p(-2, 3), q(2, 4), and r(1, -1): x = -3 p(__, ) q(, ) r(, __)

Explanation:

Step1: Recall the reflection formula

When reflecting a point \((x,y)\) over the line \(x = a\), the formula is \((x',y')=(2a - x,y)\). Here \(a=-3\).

Step2: Find the image of point \(P(-2,3)\)

Substitute \(x=-2,y = 3,a=-3\) into the formula \(x'=2a - x\). Then \(x'=2\times(-3)-(-2)=-6 + 2=-4\), \(y'=3\). So \(P'(-4,3)\).

Step3: Find the image of point \(Q(2,4)\)

Substitute \(x = 2,y = 4,a=-3\) into the formula \(x'=2a - x\). Then \(x'=2\times(-3)-2=-6-2=-8\), \(y'=4\). So \(Q'(-8,4)\).

Step4: Find the image of point \(R(1,-1)\)

Substitute \(x = 1,y=-1,a=-3\) into the formula \(x'=2a - x\). Then \(x'=2\times(-3)-1=-6 - 1=-7\), \(y'=-1\). So \(R'(-7,-1)\).

Answer:

\(P'(-4,3)\)
\(Q'(-8,4)\)
\(R'(-7,-1)\)