Question

what is the perimeter of \\( \triangle gas \\) if it has vertices with coordinates, \\( g(4,4) \\), \\( a(-2,-3) \\), and \\( s(4,-3) \\)?
23 units
25.22 units
22.22 units
24 units

Explanation:

Step1: Use the distance formula

The distance formula 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 \(GA\): \(x_1 = 4,y_1 = 4,x_2=-2,y_2=-3\)
\(GA=\sqrt{(-2 - 4)^2+(-3 - 4)^2}=\sqrt{(-6)^2+(-7)^2}=\sqrt{36 + 49}=\sqrt{85}\approx9.22\)

Step2: For \(AS\)

\(x_1=-2,y_1=-3,x_2 = 4,y_2=-3\)
\(AS=\sqrt{(4+2)^2+(-3 + 3)^2}=\sqrt{6^2+0^2}=6\)

Step3: For \(GS\)

\(x_1 = 4,y_1 = 4,x_2 = 4,y_2=-3\)
\(GS=\sqrt{(4 - 4)^2+(-3 - 4)^2}=\sqrt{0^2+(-7)^2}=7\)

Step4: Calculate the perimeter

Perimeter \(P=GA + AS+GS\approx9.22+6 + 7=22.22\)

Answer:

22.22 units