Question

determine the perimeter of the given figure on the coordinate plane. round your answer to the nearest hundredth, if necessary. triangle abc

Explanation:

Step1: Identify coordinates

Let \(A(-7,2)\), \(C(-4,2)\), \(B(-4,9)\)

Step2: Calculate length of \(AC\)

Using the distance formula for points on a horizontal line (\(y\) - coordinate is the same), \(d=\vert x_2 - x_1\vert\). Here \(AC=\vert- 4-(-7)\vert=\vert-4 + 7\vert = 3\)

Step3: Calculate length of \(BC\)

Using the distance formula for points on a vertical line (\(x\) - coordinate is the same), \(d=\vert y_2 - y_1\vert\). Here \(BC=\vert9 - 2\vert=7\)

Step4: Calculate length of \(AB\)

Use the distance formula \(d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\). For \(A(-7,2)\) and \(B(-4,9)\), \(x_1=-7,y_1 = 2,x_2=-4,y_2 = 9\). Then \(AB=\sqrt{(-4+7)^2+(9 - 2)^2}=\sqrt{3^2+7^2}=\sqrt{9 + 49}=\sqrt{58}\approx7.62\)

Step5: Calculate perimeter

Perimeter \(P=AC + BC+AB\). Substitute the values: \(P=3 + 7+7.62=17.62\)

Answer:

\(17.62\)