Question

Find the perimeter of a quadrilateral with the following vertices

(−6, −2), (0, −10), (5, 2), (−1, 10)
(1 point)
Responses

40
40

46
46

52
52

23

Answer 1

To find the perimeter of a quadrilateral, we add up the lengths of all four sides.

First, let's calculate the length of the first side:
Distance between (-6, -2) and (0, -10) = √[(0 - (-6))^2 + (-10 - (-2))^2] = √[6^2 + (-8)^2] = √[36 + 64] = √100 = 10

Next, let's calculate the length of the second side:
Distance between (0, -10) and (5, 2) = √[(5 - 0)^2 + (2 - (-10))^2] = √[5^2 + 12^2] = √[25 + 144] = √169 = 13

Next, let's calculate the length of the third side:
Distance between (5, 2) and (-1, 10) = √[(-1 - 5)^2 + (10 - 2)^2] = √[(-6)^2 + 8^2] = √[36 + 64] = √100 = 10

Lastly, let's calculate the length of the fourth side:
Distance between (-1, 10) and (-6, -2) = √[(-6 - (-1))^2 + (-2 - 10)^2] = √[(-5)^2 + (-12)^2] = √[25 + 144] = √169 = 13

Adding up all four side lengths, we get:
10 + 13 + 10 + 13 = 46

Therefore, the perimeter of the quadrilateral is 46.