Respuesta :

gmany

The formula of a midpoint:

[tex]M_{AB}\left(\dfrac{x_A+x_B}{2},\ \dfrac{y_A+y_B}{2}\right)[/tex]

We have

[tex]M(3,\ 7)\to x_M=3,\ y_M=7\\\\A(5,\ 1)\to x_A=3,\ y_A=7[/tex]

Substitute:

[tex]\dfrac{5+x_B}{2}=3\qquad|\cdot2\\\\5+x_B=6\qquad|-5\\\\x_B=1\\\\\dfrac{1+y_B}{2}=7\qquad|\cdot2\\\\1+y_B=14\qquad|-1\\\\y_B=13[/tex]

Answer: B(1, 13)

Supriti
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)