Question

What is the other endpoint if (1,-2) is an endpoint and (5,-5) is a midpoint?

A) (9, -8)
B) (3, -8)
C) (9, -2)
D) (3, -2)

Answer 1

D) (3,-2) is the answer of this question

Answer 2

To find the other endpoint when you have one endpoint and the midpoint, you calculate the averages of the x and y coordinates separately and solve for the unknowns. In this case, the other endpoint is (9, -8).

Step-by-step explanation:

To find the other endpoint of a line segment, we can use the midpoint formula which is, in essence, the average of the endpoints. Since we know the midpoint (5, -5) and one endpoint (1, -2), we can find the other endpoint by setting up equations based on the idea that the midpoint coordinates are the averages of the corresponding coordinates of the endpoints.

Let's label our unknown endpoint as (x, y). To find the x-coordinate of the other endpoint:

1 + x = 2 × 5 (because the midpoint x-coordinate is the average of the endpoint x-coordinates)
1 + x = 10
x = 9

To find the y-coordinate of the other endpoint:

-2 + y = 2 × (-5) (because the midpoint y-coordinate is the average of the endpoint y-coordinates)
-2 + y = -10
y = -8

Therefore, the other endpoint is (9, -8), which corresponds to option A.