Question

Given two vertices of a triangle (3, -4) and (-2, 0) and the centroid (5, -1), what are the possible coordinates of the third vertex of the triangle?

A) (0, 2)

B) (2, -2)

C) (4, -3)

D) (-3, 2)

Answer 1

The possible coordinates of the third vertex of the triangle are (1/2, -2), which is approximately equal to (0.5, -2).

Step-by-step explanation:

To find the possible coordinates of the third vertex of the triangle, we can use the formula for finding the centroid of a triangle. The centroid is the average of the coordinates of the three vertices. So, if the centroid is (5, -1) and two vertices are (3, -4) and (-2, 0), we can find the third vertex by taking the average of the x-coordinates and the average of the y-coordinates.

The average of the x-coordinates is (3 + -2) / 2 = 1/2, and the average of the y-coordinates is (-4 + 0) / 2 = -2. So, the coordinates of the third vertex are (1/2, -2).

Therefore, the correct answer is B) (2, -2).