Given the line segment AB with endpoints A (-7,8) and midpoint M (-2, -1), determine a) the length of AM b) the coordinates of endpoint

Question

Given the line segment AB with endpoints A (-7,8) and midpoint M (-2, -1), determine a) the length of AM b) the coordinates of endpoint

Answer 1

We can find the length of AM by setting up a right triangle in the coordinate plane and solving for the hypotenuse with Pythagorean Theorem. The lengths of the legs are the differences in the x- and y-coordinates.

 

So we get that (-1-8)²+(-2--7)²=AM²

(-9)²+(5)²=AM²

81+25=AM²

106=AM²

AM=√(106)≈10.30

 

Now, we want to find the coordinates of B. Recognize that we must have gone half the x-distance and half the y-distance to get from A to M.

 

For the x-coordinate, we went from -7 to -2, which is 5 units right. So we go another 5 units right to get to x=3.

For the y-coordinate, we went from 8 to -1, which is 9 units down. So we go another 9 units down to get to y=-10.

 

So the coordinates of B are (3, -10).