Question

If the midpoint of the line segment ‾AB is M(−2,6), and the coordinates of point A are (−3,8), what are the coordinates of point B?

Answer 1

The coordinates of point B are (−1,4).

To find the coordinates of point B, you can use the midpoint formula. The midpoint formula for a line segment with endpoints (x1,y1 ) and (x2 ,y2 ) is given by:

Midpoint=( x1 +x2/2 , y1 +y2/2 )

In this case, the midpoint M is given as (xM ,yM)=(−2,6), and the coordinates of point A are (x1 ,y1 )=(−3,8). Let the coordinates of point B be (x2 ,y2 ).

Now, we can set up the equations based on the midpoint formula:

xM= x1+x2/2

yM= y1 +y2/ 2

​Plugging in the values, we get:

-2= (-3+x_2)/2

6= (8+y_2)/2

Solving these equations will give you the coordinates of point B:

-2= -3x_2/ 2

​-4 =−3+x_2

​x_2=−1

So, the x-coordinate of point B is −1. Now, substitute this into the second equation:

6= 8+y_2/ 2

12=8+y_2

y_2=4

​ Therefore, the coordinates of point B are (−1,4).