Question

use the coordinates to compute the perimeter of the triangle. (1 point) 10.8 units 11.2 units 10 units 12 units

Explanation:

Step1: Calculate the length of the base

The base is between \((1,1)\) and \((5,1)\). Using the distance formula \(d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\), here \(y_1 = y_2 = 1\), so \(d=\vert5 - 1\vert=4\)

Step2: Calculate the length of the other two sides

For the side between \((1,1)\) and \((3,4)\):
\(d=\sqrt{(3 - 1)^2+(4 - 1)^2}=\sqrt{4 + 9}=\sqrt{13}\approx3.6\)
For the side between \((3,4)\) and \((5,1)\):
\(d=\sqrt{(5 - 3)^2+(1 - 4)^2}=\sqrt{4 + 9}=\sqrt{13}\approx3.6\)

Step3: Calculate the perimeter

Perimeter \(P = 4+3.6+3.6 = 11.2\)

Answer:

11.2 units