Question

The midpoint of AB is (3,7). The coordinate of one endpoint is A(5,1). Find the coordinate of endpoint B. Show or explain work.

Answer 1

The formula of a midpoint:

`M_(AB)\left((x_A+x_B)/(2),\ (y_A+y_B)/(2)\right)`

We have

`M(3,\ 7)\to x_M=3,\ y_M=7\\\\A(5,\ 1)\to x_A=3,\ y_A=7`

Substitute:

`(5+x_B)/(2)=3\qquad|\cdot2\\\\5+x_B=6\qquad|-5\\\\x_B=1\\\\(1+y_B)/(2)=7\qquad|\cdot2\\\\1+y_B=14\qquad|-1\\\\y_B=13`

Answer: B(1, 13)

Answer 2

We have a line AB with point P
A(5,1) which becomes (x1,y1)
P(3,7) which becomes (x,y)
B(x,y) which becomes (x2,y2)

Since it is a midpoint, we can use the midpoint formula directly.

x = (x1+x2)/2

3 = (5+x)/2
x=1
Thus our x coordinate is 1

y = (y1+y2)/2

7 = (1+y)/2
y=13
Thus our y coordinate is 13

Our answer is B(1,13)