Question

The midpoint M of VW has coordinates (4, 0). Point W has coordinates (5, -6). Find the

coordinates of point V.

Answer 1

To find the coordinates of point V, use the midpoint formula with known midpoint M and endpoint W coordinates. Solving the calculations, the coordinates of point V are found to be (3, 6).

Step-by-step explanation:

The question asks to find the coordinates of point V given that the midpoint M of the line segment VW is at (4, 0) and point W is at (5, -6). The midpoint formula states that the x-coordinate of the midpoint is the average of the x-coordinates of the two endpoints and the y-coordinate of the midpoint is the average of the y-coordinates of the two endpoints. So, we can set up equations to find the x and y coordinates of V using the facts that:

Midpoint x-coordinate = (Vx + Wx) / 2

Midpoint y-coordinate = (Vy + Wy) / 2

Step-by-Step Calculation

Midpoint M's x-coordinate is 4, so we have (Vx + 5) / 2 = 4. Solving for Vx gives us Vx = 2(4) - 5 = 3.

1. Midpoint M's y-coordinate is 0, so we have (Vy - 6) / 2 = 0. Solving for Vy gives us Vy = 2(0) + 6 = 6.

Therefore, the coordinates of point V are (3, 6).