Question

The coordinates of triangle GBW are G (20, 10) B (-35, 20), and W (5,-10). Is GBW a right triangle? Justify your answer.

Answer 1

We know from Pythagoras' Theorem, a right angle triangle can be identified by the relationship:

$a^2+b^2=c^2$

Thus, we know if the side lengths of the triangle in question abide by this relation, the triangle is right.

First, we must find the greatest side length.

We know, using the distance formula.

$GB= \sqrt{(-35-20)^2 +(20-10)^2} =\sqrt{3125}$
$BW= \sqrt{(5+35)^2 +(-10-20)^2} =\sqrt{2500}$
$WG= \sqrt{(20-5)^2 +(10+10)^2} =\sqrt{625}$

From this, we know that:
$GB\ \textgreater \ BW\ \textgreater \ WG$
Therefore, GB would be the hypotenuse of the triangle.
Now we substitute the values for the two shorter lengths and the greater length into the pythagorean theorem:
$a^2+b^2=2500+625=3125$
$c^2=3125$
$\therefore LHS=RHS$
Therefore, this triangle is a right angled triangle