Question

M is the midpoint of line segment AB. If the coordinates of M are (2, 6) and the coordinates of B are (5, 10), which of the following represents the coordinates of point A?

Answer 1

The coordinates are A(-1,2)

Explanation:

we know that

The formula to calculate the midpoint between two points is equal to

`M=((x_1+x_2)/(2),(y_1+y_2)/(2))`

In this problem we have

`M(2,6)\\A(x_1,y_1)`

`B(x_2,y_2) ---> B(5,10)`

substitute the given values

`(2,6)=((x_1+5)/(2),(y_1+10)/(2))`

Solve for
`x_1`

`2=(x_1+5)/2\\4=x_1+5\\x_1=4-5=-1`

Solve for
`y_1`

`6=(y_1+10)/2\\12=y_1+10\\y_1=12-10=2`

therefore

The coordinates are A(-1,2)