Question

graph the following figure in the coordinate plane. find the perimeter.
a(-6, -6), b(2,0), c(2, -7)
...
choose the correct graph on the right.
the perimeter of δabc is \\(\square\\) units.
(type an exact answer, using radicals as needed.)

Explanation:

Step1: Find length of BC

Points B(2,0) and C(2,-7) have same x - coordinate. So length \( BC=\vert0 - (-7)\vert = 7\)

Step2: Find length of AB

Using distance formula \(d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\) for A(-6,-6) and B(2,0):
\(AB=\sqrt{(2 - (-6))^2+(0 - (-6))^2}=\sqrt{8^2 + 6^2}=\sqrt{64 + 36}=\sqrt{100}=10\)

Step3: Find length of AC

Using distance formula for A(-6,-6) and C(2,-7):
\(AC=\sqrt{(2 - (-6))^2+(-7 - (-6))^2}=\sqrt{8^2+(-1)^2}=\sqrt{64 + 1}=\sqrt{65}\)

Step4: Find perimeter

Perimeter \(=AB + BC+AC=10 + 7+\sqrt{65}=17+\sqrt{65}\)

Answer:

\(17+\sqrt{65}\)