Question

type the correct answer in the box. use numerals instead of words. if necessary, use / for the fraction bar.
what is the perimeter of \\( \triangle efg \\) shown in the coordinate grid? round your answer to the nearest whole unit.

the perimeter of triangle efg is approximately units.

Explanation:

Step1: Find coordinates of points

Coordinates: \(E(-7,9)\), \(F(1,3)\), \(G(-5,-5)\)

Step2: Calculate distance \(EF\)

Use distance formula \(d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\)
\(EF=\sqrt{(1 - (-7))^2+(3 - 9)^2}=\sqrt{8^2+(-6)^2}=\sqrt{64 + 36}=\sqrt{100}=10\)

Step3: Calculate distance \(FG\)

\(FG=\sqrt{(-5 - 1)^2+(-5 - 3)^2}=\sqrt{(-6)^2+(-8)^2}=\sqrt{36+64}=\sqrt{100}=10\)

Step4: Calculate distance \(EG\)

\(EG=\sqrt{(-5 - (-7))^2+(-5 - 9)^2}=\sqrt{2^2+(-14)^2}=\sqrt{4 + 196}=\sqrt{200}\approx14.14\)

Step5: Calculate perimeter

Perimeter \(P=EF + FG+EG\approx10 + 10+14.14 = 34.14\)

Answer:

34