SOLUTION: 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 tr

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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)
Answer by Edwin McCravy(20060)   (Show Source): You can put this solution on YOUR website!
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)
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  AC2 + AB2 = BC2
               80  +  45 = 125 

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

Edwin
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