Question

suppose a triangle is drawn on a coordinate plane. using vertices with the coordinates (1, 1), (4, 1), and (5, 4), compute the perimeter. round your answer to the nearest tenth. (1 point)
○ 12 units
○ 10.5 units
○ 11.2 units
○ 11 units

Explanation:

Step1: Find the length of the first side

Use the distance formula \(d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\). For points \((1,1)\) and \((4,1)\):
\(d_1=\sqrt{(4 - 1)^2+(1 - 1)^2}=\sqrt{3^2+0^2}=\sqrt{9}=3\)

Step2: Find the length of the second side

For points \((4,1)\) and \((5,4)\):
\(d_2=\sqrt{(5 - 4)^2+(4 - 1)^2}=\sqrt{1^2+3^2}=\sqrt{1 + 9}=\sqrt{10}\approx3.2\)

Step3: Find the length of the third side

For points \((5,4)\) and \((1,1)\):
\(d_3=\sqrt{(1 - 5)^2+(1 - 4)^2}=\sqrt{(-4)^2+(-3)^2}=\sqrt{16 + 9}=\sqrt{25}=5\)

Step4: Calculate the perimeter

\(P=d_1 + d_2 + d_3=3+3.2 + 5=11.2\)

Answer:

11.2 units