Answer:
Explanation:
To solve this problem, we need to use the distance formula to find the length of each side of the triangle, and then apply the Pythagorean theorem to determine whether the triangle is a right triangle.
Let's label the three vertices of the triangle as A, B, and C, and their coordinates as follows:
A = (-2, 5)
B = (3, -1)
C = (1, 3)
The length of AB is:
AB = sqrt((3 - (-2))^2 + (-1 - 5)^2) = sqrt(25 + 36) = sqrt(61)
The length of AC is:
AC = sqrt((1 - (-2))^2 + (3 - 5)^2) = sqrt(9 + 4) = sqrt(13)
The length of BC is:
BC = sqrt((1 - 3)^2 + (3 - (-1))^2) = sqrt(4 + 16) = sqrt(20) = 2sqrt(5)
Now, we need to check whether the triangle is a right triangle. We can do this by checking whether the sum of the squares of the two shorter sides (AB and AC) is equal to the square of the longest side (BC). If it is, then the triangle is a right triangle.
AB^2 + AC^2 = 61 + 13 = 74
BC^2 = (2sqrt(5))^2 = 20
Since AB^2 + AC^2 is not equal to BC^2, the triangle is not a right triangle.
Therefore, the answer is: "The triangle is not a right triangle."