Question

AB is M(3,-2). One endpoint is A(7,-9). Find the coordinates of the other endpoint B.

Answer 1

The required points of the given line segment are ( - 1, - 5 ).

Explanation:

Given that the line segment AB whose midpoint M is ( 3, -2 ) and point A is ( 7, - 9), then we have to find point B 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 M are-

M = (
`( x_(1) + x_(2) )/(2)` ,
`( y_(1) + y_(2) )/(2)` )

Here,

Let A ( 7, - 9 ), B ( x, y ) with midpoint M ( 3, - 2 ) -

then by the midpoint formula M are-

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

On comparing x coordinate and y coordinate -

We get,

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

( 7 + x = 6, - 9 + y = - 4 )

( x = 6 - 7, y = - 4 + 9 )

( x = - 1, y = -5 )

Hence the required points A are ( - 1, - 5 ).

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