Question

practice - perimeter on the coordinate plane

1. find the perimeter of δdef. round to the nearest tenth if necessary.

d(-5, 2), e(4, 6), f(2, -3)

Explanation:

Step1: Find length of DE

Use distance formula $d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$. For $D(-5,2)$ and $E(4,6)$:
$DE = \sqrt{(4 - (-5))^2 + (6 - 2)^2} = \sqrt{9^2 + 4^2} = \sqrt{81 + 16} = \sqrt{97} \approx 9.8$

Step2: Find length of EF

For $E(4,6)$ and $F(2,-3)$:
$EF = \sqrt{(2 - 4)^2 + (-3 - 6)^2} = \sqrt{(-2)^2 + (-9)^2} = \sqrt{4 + 81} = \sqrt{85} \approx 9.2$

Step3: Find length of FD

For $F(2,-3)$ and $D(-5,2)$:
$FD = \sqrt{(-5 - 2)^2 + (2 - (-3))^2} = \sqrt{(-7)^2 + 5^2} = \sqrt{49 + 25} = \sqrt{74} \approx 8.6$

Step4: Calculate perimeter

Perimeter = $DE + EF + FD \approx 9.8 + 9.2 + 8.6 = 27.6$

Answer:

27.6