Question

M(3,2) is the midpoint of segment AB. B(-2,5). What are the coordinates of A

Answer 1

The required points of the given line segment are ( 8, -1 ).

Explanation:

Given that the line segment AB whose midpoint M is ( 3, 2 ) and point B is ( -2, 5), then we have to find point A of the line segment AB-

As we know that-

If a line segment AB is with endpoints (
`x_(1), y_(1)` ) and (
`x_(2), y_(2)` )then the mid points C are-

C = (
`(x_(1) + x_(2) )/(2)` ,
`\frac{ y_(1) + y_(2)} {2}` )

Here,

Let A ( x, y ), B ( -2, 5 ) with midpoint M ( 3, 2 )-

then by the midpoint formula C are-

( 3, 2 ) = (
`(x - 2)/(2)` ,
`( y + 5)/(2)` )

On comparing x coordinate and y coordinate -

We get,

(
`(x - 2)/(2)` = 3 ,
`(y + 5)/(2)` = 2)

( x - 2 = 6, y + 5 = 4 )

( x = 6 + 2, y = 4 - 5 )

( x = 8, y = -1 )

Hence the required points A are (8, -1 ).

We can also verify by putting these points into Midpoint formula.