Question

The coordinates of the endpoints of overline TU are T-2,7 and U4,-8 . Point V is on overline TU and divides it such that TV:UV is 1:2 What are the coordinates of V?

Answer 1

To find the coordinates of point V that divides the line segment TU in the ratio 1:2, the section formula is used, giving the coordinates of V as (0, 2).

Step-by-step explanation:

The coordinates of the endpoints of überline TU are T(-2,7) and U(4,-8). To find point V that divides the line segment TU in the ratio 1:2, we use the section formula for internal division. The coordinates of point V can be calculated using the following formulas:

• x-coordinate of V = (1*x2 + 2*x1) / (1 + 2)
• y-coordinate of V = (1*y2 + 2*y1) / (1 + 2)

Substituting the values, we get:

• x-coordinate of V = (1*4 + 2*(-2)) / 3 = (4 - 4) / 3 = 0 / 3 = 0
• y-coordinate of V = (1*(-8) + 2*7) / 3 = (-8 + 14) / 3 = 6 / 3 = 2

Therefore, the coordinates of V are (0, 2).