Determine whether the triangle with vertices A (-1, 7), B (10, -4), and C (12, -2) is a right triangle and explain your findings.

Answer 1

A(-1,7), B(10,-4), and C(12,-2) are vertices of a triangle

AB has slope= (7+4)/(-1-10) = -11/11= -1

BC has slope =(-2+4)/(12-10) = 2/2 = 1

AC has slope = (7+2)/(-1-12) = -9/13

AB and BC slopes are negative inverses

to be a right triangle requires two perpendicular sides

the triangle is a right triangle.

-1 and 1 are negative inverse slopes

-1/1 = the negative inverse of +1/1

or

alternative approach is calculate the distances of AB, BC, and AC

and see if the longest side squared = the sum of squares of the other two sides

if that equality holds true, it's a right triangle.

AB =11sqr2

BC =2sqr2

AC = sqr(81+169)=sqr250

AC^2 = BC^2+ AB^2

250 = 121(2) + 4(2)

250 = 242 + 8

AC is the hypotenuse of the right triangle