A right triangle has vertices (−7,9),(3,9), (−7,−15)
Find the perimeter of the triangle.(1 point)
Responses
17
17
60
60
24
24
38
38
To find the perimeter of a triangle, we need to find the lengths of its sides.
Using the distance formula, we can find the lengths of the sides of the triangle.
Side 1: Length between (-7, 9) and (3, 9)
Distance = √[(x2 - x1)^2 + (y2 - y1)^2] = √[(3 - (-7))^2 + (9 - 9)^2]
Distance = √[10^2 + 0^2] = √(100) = 10
Side 2: Length between (-7, 9) and (-7, -15)
Distance = √[(x2 - x1)^2 + (y2 - y1)^2] = √[(-7 - (-7))^2 + (-15 - 9)^2]
Distance = √[0^2 + (-15 - 9)^2] = √[(-24)^2] = √(576) = 24
Side 3: Length between (3, 9) and (-7, -15)
Distance = √[(x2 - x1)^2 + (y2 - y1)^2] = √[(3 - (-7))^2 + (9 - (-15))^2]
Distance = √[10^2 + (9 + 15)^2] = √[100 + 24^2] = √[676] = 26
Adding up the lengths of all sides, we get:
10 + 24 + 26 = 60
Therefore, the perimeter of the triangle is 60.