Question 1171406
Three points, A, B and C are plotted on the Cartesian plane and connected to
form a triangle. Point A is on the x-axis at -4, point B is (-1, -6) and point
C is (4, 4). Is this triangle a right triangle with the hypotenuse being formed
by the line that connects B and C? Explain why or why not. Algebraically show
your work to determine this. (You do not graph these points)
<pre>
There are two ways to show this.

The easy way is to use the slope formula to show that the slope of AC is 1/2,
and the slope of AB is -2, and they are perpendicular because the product of
their slopes is -1 (They are negative reciprocals).

The harder way is to use the distance formula to find the three sides

Then show that  AC<sup>2</sup> + AB<sup>2</sup> = BC<sup>2</sup>
               80  +  45 = 125 

Then it is a right triangle by the converse of the Pythagorean theorem.

Edwin</pre>