area of a triangle with vertices

hi,

i need to prove that the triangle with vertices (-2,8), (3,20) and (11,8) is isoceles. Find its area.

now for this question would i just need to draw it on a graph and dop;

BxH/2

13x12=156/2=78

if this is correct so far im unsure what to do after this point to find that it is isoceles.

help is required please!

thanks!

Re: area of a triangle with vertices

Quote:

Originally Posted by

**andyboy179** i need to prove that the triangle with vertices (-2,8), (3,20) and (11,8) is isoceles. Find its area.

You can find the length of each side.

The use the semi-perimeter rule to find the area.

Re: area of a triangle with vertices

i don't know what the semi-perimeter rule is.

Re: area of a triangle with vertices

Hello, andyboy179!

Quote:

Prove that the triangle with vertices A(-2,8), B(3,20) and C(11,8) is isoceles.

Find its area.

For this question, would i just need to draw it on a graph and do:

. . $\displaystyle \text{Area} \:=\:\tfrac{1}{2}bh \:=\:\tfrac{1}{2}(13)(12) \:=\:78\;?$ . . . . Yes!

If this is correct so far, I;m unsure what to do after this point to find that it is isoceles.

Excellent work!

We see that $\displaystyle AC$ is horizontal and $\displaystyle AC = 13.$

And we find that the altitude from $\displaystyle B$ is 12.

An isosceles triangle has two equal sides.

Use the Distance Formula on side $\displaystyle AB.$

. . You'll find that it too is 13 units long.

(We also find that $\displaystyle BC$ is *not* 13 units long.

Hence, the triangle is *not* equilateral.)

Re: area of a triangle with vertices

Quote:

Originally Posted by

**Soroban** Hello, andyboy179!

Excellent work!

We see that $\displaystyle AC$ is horizontal and $\displaystyle AC = 13.$

And we find that the altitude from $\displaystyle B$ is 12.

An isosceles triangle has two equal sides.

Use the Distance Formula on side $\displaystyle AB.$

. . You'll find that it too is 13 units long.

(We also find that $\displaystyle BC$ is *not* 13 units long.

Hence, the triangle is *not* equilateral.)

hi, how do i use the distace formula on side AB?

Re: area of a triangle with vertices

sorry i know how to do it!!! mental block!! thanks alot for the answer!!!!