Question

A triangle has vertices p(-3,1), q(6,3) and r(1,8). Determine if ∆pqr is a right angle triangle

Answer 1

To determine if ∆pqr is a right angle triangle, we need to check if any of the three angles in the triangle is equal to 90 degrees. Using the concept of slope, we can find the slopes of the three sides of the triangle and compare them to see if any of them are equal to 90 degrees.

Step-by-step explanation:

To determine if ∆pqr is a right angle triangle, we need to check if any of the three angles in the triangle is equal to 90 degrees. We can use the concept of slope to find the angles.

Using the formula for slope (m = (y2 - y1) / (x2 - x1)), we can find the slopes of the three sides of the triangle:

mpq = (3 - 1) / (6 - (-3)) = 2 / 9

mqr = (8 - 3) / (1 - 6) = 5 / -5 = -1

mrp = (8 - 1) / (1 - (-3)) = 7 / 4

Since mqr is negative, we need to take the absolute value when comparing it to the other slopes.

Comparing mpq, mqr, and mrp, none of them are equal to 90 degrees, so ∆pqr is not a right angle triangle.