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Question

Question
What is the perimeter of triangle A B Cwith vertices A left-parenthesis negative 2 comma 9 right-parenthesis, B left-parenthesis 7 comma negative 3 right-parenthesis, and C left-parenthesis negative 2 comma negative 3 right-parenthesis in the coordinate plane?
(1 point)
Responses

21 units
21 units

15 units
15 units

34 units
34 units

36 units

Answer 1

To find the perimeter of a triangle, we need to find the distance between each pair of vertices and then sum them up.

The distance between points A(-2,9) and B(7,-3) can be found using the distance formula: d = √((x2 - x1)^2 + (y2 - y1)^2)
d = √((7 - (-2))^2 + (-3 - 9)^2) = √((9)^2 + (-12)^2) = √(81 + 144) = √225 = 15

The distance between points B(7,-3) and C(-2,-3) can be found using the distance formula: d = √((x2 - x1)^2 + (y2 - y1)^2)
d = √((-2 - 7)^2 + (-3 - (-3))^2) = √((-9)^2 + (0)^2) = √(81 + 0) = √81 = 9

The distance between points C(-2,-3) and A(-2,9) can be found using the distance formula: d = √((x2 - x1)^2 + (y2 - y1)^2)
d = √((-2 - (-2))^2 + (9 - (-3))^2) = √((0)^2 + (12)^2) = √(0 + 144) = √144 = 12

Now, let's find the perimeter by summing up the distances:
Perimeter = 15 + 9 + 12 = 36

Therefore, the perimeter of triangle ABC is 36 units. The correct answer is 36 units.