Question

Which of the following coordinates is the other endpoint of a line segment if one endpoint is at (4, -10) and the midpoint is at (-7, 12)?

A) (-18, 34)
B) (-18, -34)
C) (18, -34)
D) (18, 34)

Answer 1

To find the other endpoint of a line segment when one endpoint and the midpoint are given, the midpoint formula can be rearranged and used to calculate the coordinates of the unknown endpoint. The correct coordinates for the endpoint are (-18, 34), corresponding to option A.

Step-by-step explanation:

The student is asking how to find the endpoint of a line segment when given one endpoint and the midpoint. To find the other endpoint, we can use the midpoint formula. The midpoint M(x,y) of a line segment with endpoints A(x1,y1) and B(x2,y2) is given by:

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

We can rearrange this formula to solve for the unknown endpoint:

B = (2*M - A).

Substituting the known endpoint A(4, -10) and midpoint M(-7, 12), we get:

Bx = 2*(-7) - 4 = -18
By = 2*12 - (-10) = 34

So, the coordinates of point B are (-18, 34).

The correct answer is option A) (-18, 34).