Question

A triangle is graphed in the coordinate plane. The vertices of the triangle have coordinates (–3, 1), (1, 1), and (1, –2). What is the perimeter of the triangle?

Answer 1

The perimeter of the triangle is
`12\ units`

Explanation:

Let

`A(-3,1),B(1,1),C(1,-2)`

we know that

The perimeter of triangle is equal to

`P=AB+BC+AC`

the formula to calculate the distance between two points is equal to

`d=\sqrt{(y2-y1)^(2)+(x2-x1)^(2)}`

step 1

Find the distance AB

`A(-3,1),B(1,1)`

substitute in the formula

`AB=\sqrt{(1-1)^(2)+(1+3)^(2)}`

`AB=\sqrt{(0)^(2)+(4)^(2)}`

`AB=4\ units`

step 2

Find the distance BC

`B(1,1),C(1,-2)`

substitute in the formula

`BC=\sqrt{(-2-1)^(2)+(1-1)^(2)}`

`BC=\sqrt{(-3)^(2)+(0)^(2)}`

`BC=3\ units`

step 3

Find the distance AC

`A(-3,1),C(1,-2)`

substitute in the formula

`AC=\sqrt{(-2-1)^(2)+(1+3)^(2)}`

`AC=\sqrt{(-3)^(2)+(4)^(2)}`

`AC=5\ units`

step 4

Find the perimeter

`P=AB+BC+AC`

substitute the values

`P=4+3+5=12\ units`