SOLUTION: Determine if the points (3,5), (3,3) and (2,4) are the vertices of a right triangle. Explain your rationale.

Question 1195474: Determine if the points (3,5), (3,3) and (2,4) are the vertices of a right triangle. Explain your rationale.
Found 2 solutions by Alan3354, ikleyn:
Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
Determine if the points A(3,5), B(3,3) and C(2,4) are the vertices of a right triangle. Explain your rationale.
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Slope of AC = diffy/diffx = (3-2)/(5-4) = 1
Slope of BC = ((3-2)/(3-4) = -1
---> perpendicular --> a right triangle
Answer by ikleyn(52873) (Show Source): You can put this solution on YOUR website!
.
Determine if the points (3,5), (3,3) and (2,4) are the vertices of a right triangle.
Explain your rationale.
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Points A = (3,5) and B = (3,3) have the same x-coordinate. It means that both points A and B lie on vertical line x= 3, parallel to y-axis. Next, points A = (3,5) and C = (2,4) have different y-coordinates; hence, line AC is not horizontal. Similarly, points B = (3,3) and C = (2,4) have different y-coordinates; hence, line BC is not horizontal. Thus, line AB is vertical, but angles A and B are not right angles. So, we only should check if lines AC and BC are perpendicular. Line AC has the slope = = 1. Line BC has the slope = = -1. Thus lines AC and BC are perpendicular, since their slopes are 1 and -1, i.e. negatively reciprocal (their product is 1 * (-1) = -1). ANSWER. Angle C is the right angle.

Solved.

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