Question

Determine whether this is a right triangle
vertices: G(1, -1) H(5, 0) and J(3, 8)

Should I use distance formula to find the sides and use Pythagorean theorem to prove it? Or is there another method?

Thanks.

Answer 1

There are other methods (such as computing and comparing the slopes of the three lines) but I like your way.
GH^2 = 17
HJ^2 = 68
GJ^2 = 85
Looks like the Pythagorean theorem works. GJ is the hypotenuse.

Answer 2

The easiest way is to use the distance formula for points in the (x,y) form.

Use the formula 3 times.

You have triangle GHJ.

Use the formula from point:

G to H

H to J

G to J

Only then will you be able to tell if triangle GHJ is a right triangle or not.

Answer 3

given vertices of triangle G(1,-1),
H(5,0),J(3,8)
first find distance between G to H
i.e root of 5-1 whole square+root of 0-(-1) whole square
similarly find from H to J &Jto G
apply right angle theorm