Question

use the given coordinates to compute the perimeter of the triangle
round your answer to the nearest tenth.
(1 point)
the perimeter is approximately units.

Explanation:

Step1: Calculate the length of \(PQ\)

The formula for the distance between two points \((x_1,y_1)\) and \((x_2,y_2)\) is \(d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\). For \(P(1,2)\) and \(Q(1,6)\), \(x_1 = 1,y_1=2,x_2 = 1,y_2 = 6\).
\(PQ=\sqrt{(1 - 1)^2+(6 - 2)^2}=\sqrt{0 + 16}=4\)

Step2: Calculate the length of \(PR\)

For \(P(1,2)\) and \(R(-4,2)\), \(x_1 = 1,y_1=2,x_2=-4,y_2 = 2\).
\(PR=\sqrt{(-4 - 1)^2+(2 - 2)^2}=\sqrt{(-5)^2+0}=5\)

Step3: Calculate the length of \(QR\)

For \(Q(1,6)\) and \(R(-4,2)\), \(x_1 = 1,y_1=6,x_2=-4,y_2 = 2\).
\(QR=\sqrt{(-4 - 1)^2+(2 - 6)^2}=\sqrt{(-5)^2+(-4)^2}=\sqrt{25 + 16}=\sqrt{41}\approx6.4\)

Step4: Calculate the perimeter \(C\)

The perimeter \(C=PQ + PR+QR\).
\(C=4 + 5+6.4=15.4\)

Answer:

\(15.4\)