Question

the coordinates of vertices of triangle abc are a(1,4) b(-2,-1) and c(-3,-2) find the perimeter of abc leave your answer in simplest radical form

Answer 1

Answer:
`√(34)+√(2)+2√(13)`

Step-by-step explanation

We'll need the side lengths to get the perimeter.

To get each side length, we use the distance formula.

This is because the distance from A to B is the same as the length of segment AB.

Let's use the distance formula to find out how far it is from A to B.

`A = (x_1,y_1) = (1,4) \text{ and } B = (x_2, y_2) = (-2,-1)\\\\d = \text{ distance from A to B} = \text{ length of segment AB}\\\\d = √((x_1 - x_2)^2 + (y_1 - y_2)^2)\\\\d = √((1-(-2))^2 + (4-(-1))^2)\\\\d = √((1+2)^2 + (4+1)^2)\\\\d = √((3)^2 + (5)^2)\\\\d = √(9 + 25)\\\\d = √(34)\\\\d \approx 5.830952\\\\`

Segment AB is exactly
`√(34)` units long (which approximates to roughly 5.830952 units).

Follow similar steps to find the other exact side lengths are
`BC = √(2)` and
`AC = 2√(13)`

Then we add up the sides to get the perimeter.

`AB+BC+AC = √(34)+√(2)+2√(13)`