Question

What is the endpoint if the midpoint is (8, 14) and the other endpoint is (16, 17)?

Options to complete the question:

a. (0, 11)
b. (0, 14)
c. (8, 10)
d. (0, 16)
e. (4, 14)

Answer 1

The missing endpoint is (0, 11), calculated by using the midpoint formula in reverse with the known midpoint (8, 14) and the given endpoint (16, 17).

Step-by-step explanation:

To find the missing endpoint when you have the midpoint and one endpoint of a line segment, you can use the midpoint formula: M = ((x1 + x2)/2, (y1 + y2)/2), where M is the midpoint and (x1, y1) and (x2, y2) are the endpoints. However, since we have one endpoint and the midpoint, we can rearrange the formula to solve for the missing endpoint.

In this case, the midpoint M is (8, 14) and one endpoint is (16, 17). To find the missing endpoint (x, y), we set up the following equations:

• (x + 16)/2 = 8
• (y + 17)/2 = 14

Solving the first equation for x:

• x + 16 = 16
• x = 16 - 16
• x = 0

And solving the second equation for y:

• y + 17 = 28
• y = 28 - 17
• y = 11

Therefore, the missing endpoint is (0, 11).