Question

The midpoint of UV is (5, -11), and the coordinates of one end point are U (3, 5). Find the coordinates of endpoint V.

a) V (7, -27)
b) V (5, -11)
c) V (9, -17)
d) V (3, -5)

Answer 1

To find the coordinates of endpoint V, use the midpoint formula with the given midpoint (5, -11) and endpoint U (3, 5). Solving the equations, we obtain the coordinates of endpoint V as (7, -27).

Step-by-step explanation:

To find the coordinates of endpoint V when you are given the midpoint of a line segment and one endpoint, you use the midpoint formula which is (x1 + x2)/2, (y1 + y2)/2. Since the midpoint of UV is (5, -11) and the coordinates of endpoint U are (3, 5), we can set up the following equations to solve for the coordinates of V: (xU + xV)/2 = xmidpoint, (yU + yV)/2 = ymidpoint. This gives us: (3 + xV)/2 = 5 , (5 + yV)/2 = -11. Solving these equations for xV and yV, we find xV = 2 × 5 - 3 = 7, yV = 2 × -11 - 5 = -27. Therefore, the coordinates of endpoint V are V (7, -27).