Question

How do you find the perimeter of the triangle whose vertices are these specific points on a plane (-1,6) (4,-5) (-2, -4)?

Answer 1

A little over `28`

Explanation:

The perimeter is going to be equal to the sum of the lengths of the sides, which can be found by using the distance formula;

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

Plugging in the points for the first two vertices, we get;

`d_1=sqrt((4+1)^2 +(-5-6)^2)=sqrt(146)~=12`

For the second two;

`d_2=sqrt((-2-4)^2+ (-4+5)^2)=sqrt(37)~=6`

And for the last pair;

`d_3=sqrt((-2+1)^2 + (-4-6)^2)=sqrt(109)~=10`

So the sum of the three sides is roughly;

`12+6+10=28`

You can get a more accurate decimal approximation by using a calculator to evaluate the square root values above instead of approximating them.