The midpoint of segment AB is M(1, 4). The coordinates of point A are (-2, 0). Find the coordinates of point B.

Question

plz help!!!!

Answer 1

Let B have coordinates (x,y); the midpoint formula tells us that x_M = ½(-2 + x) 

But since (1,4) is that midpoint, substitute 1 for x_M. 

Solve for x.

 

Similarly, for the y_M = 4 = ½(0 + y); solve for y.

 

TO CHECK, when you have the (x,y) solution, verify that the x coordinate of the midpoint really is THE AVERAGE OF THE x VALUES OF A & B.  Similarly, check that the y coordinate of the midpoint really is the average of the y values of endpoints A & B.