Question

Given the midpoint of segment Q at (2, -3) and one endpoint at (3, 2), what are the coordinates of the other endpoint?

a) (1, -8)
b) (0, -5)
c) (4, -1)
d) (-1, 8)

Answer 1

To find the other endpoint of a line segment, use the midpoint formula and the given endpoint. Solve two simple equations to find the unknown coordinates. The answer is (1, -8), option (a).

Step-by-step explanation:

To find the coordinates of the other endpoint of a line segment when given the midpoint and one endpoint, you can use the midpoint formula which is ( (x1 + x2)/2, (y1 + y2)/2 ) where (x1, y1) and (x2, y2) are the coordinates of the endpoints and the midpoint is calculated using these values. In this case, the midpoint is at (2, -3) and one endpoint is at (3, 2). Let's call the other endpoint we're trying to find as (x, y).

We set up the equations:
2 = (3 + x)/2 and -3 = (2 + y)/2

By solving the equations, we find:
x = 1 and y = -8.

Therefore, the coordinates of the other endpoint are (1, -8), which corresponds to option (a).