Question

Determine if P(5,7), Q(3,9), and R(6,8) are vertices of a right triangle.

A. Yes, they form a right triangle.
B. No, they do not form a right triangle.
C. Not enough information provided to determine.
D. Yes, but with an obtuse angle triangle.

Answer 1

Upon calculating the lengths of the sides formed by points P(5,7), Q(3,9), and R(6,8), and applying the Pythagorean theorem, it's clear that these points do not form the vertices of a right triangle. B. No, they do not form a right triangle.

Step-by-step explanation:

To determine if points P(5,7), Q(3,9), and R(6,8) form the vertices of a right triangle, one can start by calculating the lengths of the sides formed by these points. We can use the distance formula, which is derived from the Pythagorean theorem, to find the lengths of the sides PQ, PR, and QR.

The distance formula is √((x2-x1)² + (y2-y1)²), where (x1, y1) and (x2, y2) are the coordinates of two points. Applying this formula to the given points:

• PQ = √((3-5)² + (9-7)²) = √(4 + 4) = √8
• PR = √((6-5)² + (8-7)²) = √(1 + 1) = √2
• QR = √((6-3)² + (8-9)²) = √(9 + 1) = √10

Once the lengths are known, check if the Pythagorean theorem holds, a² + b² = c², for these lengths where c represents the longest side. In this case, (√8)² + (√2)² should be equal to (√10)² if it's a right triangle, which is not the case here. Therefore, the given points do not form the vertices of a right triangle, and the correct answer is B. No, they do not form a right triangle.