Question

Enter your answer and show all the steps that you use to solve this problem in the space provided. The midpoint of UV¯¯¯¯¯ is (5,−11) . The coordinates of one endpoint are U(3,5) . Find the coordinates of endpoint V.

Answer 1

To find the coordinates of endpoint V, we can use the midpoint formula. The midpoint formula states that the coordinates of the midpoint of a line segment are the average of the coordinates of the endpoints.

The midpoint formula:
Midpoint(x, y) = ((x1 + x2)/2, (y1 + y2)/2)

Given that the midpoint of UV¯¯¯¯¯ is (5, -11), and one endpoint is U(3, 5), let's substitute the values into the formula:

(5, -11) = ((3 + x)/2, (5 + y)/2)

Now, we can solve for x and y.

For x coordinate:
5 = (3 + x)/2
Multiply both sides by 2 to eliminate the fraction:
10 = 3 + x
Subtract 3 from both sides:
7 = x

For y coordinate:
-11 = (5 + y)/2
Multiply both sides by 2 to eliminate the fraction:
-22 = 5 + y
Subtract 5 from both sides:
-27 = y

Therefore, the coordinates of endpoint V are V(7, -27).