Question

Determine whether the given points (8,4) (5,7)and (-1,1) are vertices of right triangle.

Answer 1

The given points do not form a right triangle.

Step-by-step explanation:

To determine if the given points (8,4), (5,7) and (-1,1) form a right triangle, we can use the distance formula and check if the sum of the squares of the distances between the points equals the square of the distance between any two points.

Let's calculate the distances:

1. The distance between (8,4) and (5,7) is sqrt((5-8)^2 + (7-4)^2) = sqrt(9+9) = sqrt(18).
2. The distance between (5,7) and (-1,1) is sqrt((-1-5)^2 + (1-7)^2) = sqrt(36+36) = sqrt(72).
3. The distance between (8,4) and (-1,1) is sqrt((-1-8)^2 + (1-4)^2) = sqrt(81+9) = sqrt(90).

None of the sums of the squares of these distances equal the square of any of the distances, so the given points do not form a right triangle.