Question

the vertices of triangle pqr are listed below.

p(-5,8), q(-17,-1), r(-5,-10)

what is the perimeter of triangle pqr?

a. 58 units
b. 72 units
c. 48 units
d. 33 units

Explanation:

Step1: Calculate the length of \(PQ\)

Use the distance formula \(d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\).
For \(P(-5,8)\) and \(Q(-17,-1)\), \(x_1=-5,y_1 = 8,x_2=-17,y_2=-1\).

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Step2: Calculate the length of \(PR\)

For \(P(-5,8)\) and \(R(-5,-10)\), since \(x\) - coordinates are the same (\(x=-5\)), use the formula \(d=\vert y_2 - y_1\vert\).
\(PR=\vert-10 - 8\vert=\vert-18\vert = 18\)

Step3: Calculate the length of \(QR\)

For \(Q(-17,-1)\) and \(R(-5,-10)\), \(x_1=-17,y_1=-1,x_2=-5,y_2=-10\)

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Step4: Calculate the perimeter

Perimeter \(P=PQ + PR+QR\)
\(P=15 + 18+15=48\)

Answer:

C. 48 units