Question

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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:

Midpoint formula:
For a line segment with endpoints (x1, y1) and (x2, y2), the coordinates of the midpoint (M) are given by:

M = ((x1 + x2)/2, (y1 + y2)/2)

We are given that the midpoint M is (5, -11) and one endpoint U is (3, 5). Let's plug in these values into the midpoint formula and solve for V:

M = ((3 + x2)/2, (5 + y2)/2)
(5, -11) = ((3 + x2)/2, (5 + y2)/2)

Using the fact that M is (5, -11), we can write two separate equations for the x and y coordinates:

5 = (3 + x2)/2 --> equation 1
-11 = (5 + y2)/2 --> equation 2

To solve for x2, we can multiply both sides of equation 1 by 2:

10 = 3 + x2

Subtracting 3 from both sides gives us:

7 = x2

Therefore, the x-coordinate of endpoint V is 7.

To solve for y2, we can multiply both sides of equation 2 by 2:

-22 = 5 + y2

Subtracting 5 from both sides gives us:

-27 = y2

Therefore, the y-coordinate of endpoint V is -27.

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