Question

What is the perimeter, in units, of the triangle shown on the coordinate grid?

(44units

(36units

(34units

(12units​

Answer 1

36 units

Explanation:

Perimeter of the triangle is the total distances between the vertices which can be calculated as follows using distance formula where necessary:

Distance between (-1, -4) and (9, -4):

This can be calculated without using the distance formula.

The distance between both vertices = |9 -(-1)| = 10 units

Distance between (-1, -4) and (4, 8):

`d = √((x_2 - x_1)^2 + (y_2 - y_1)^2)`

Let,

`(-1, -4) = (x_1, y_1)`

`(4, 8) = (x_2, y_2)`

`d = √((4 -(-1))^2 + (8 - (-4))^2)`

`d = √((5)^2 + (12)^2)`

`d = √(25 + 144) = √(169)`

`d = 13 units`

Distance between (9, -4) and (4, 8):

`d = √((x_2 - x_1)^2 + (y_2 - y_1)^2)`

Let,

`(9, -4) = (x_1, y_1)`

`(4, 8) = (x_2, y_2)`

`d = √((4 - 9)^2 + (8 - (-4))^2)`

`d = √((-5)^2 + (12)^2)`

`d = √(25 + 144) = √(169)`

`d = 13 units`

Perimeter = 10 + 13 + 13 = 36 units