Question

12. The midpoint of AB is M(9,7). One endpoint is A(3,9). Find the coordinates of endpoint B.

Answer 1

Answer:

The coordinates of endpoint B are (15, 5).

Step-by-step explanation:

This problem gives you the midpoint coordinates of line segment AB, and the coordinates of endpoint A. Given this, you can find the "distance" between the two points and thus the "distance" between the midpoint and point B.

Start by subtracting the the coordinates of point A from the coordinates of the midpoint.

X: 9-3=6

Y: 7-9=-2

X travels along the horizontal axis, while Y travels along the vertical axis. This means that a positive X goes right, a negative X goes left, a positive Y goes up, and a negative Y goes down.

Because you have a positive 6 for X, the line traveled 6 units right from point A to the midpoint. And because you have a negative 2 for Y, the line traveled 2 units down from point A to the midpoint.

Now, going from the midpoint to your unknown point B is simply shifting the discovered number of units right and down, or adding and subtracting from your midpoint accordingly.

M(9, 7)

B(9+6, 7-2)

B(15, 5)