Question

Find the other endpoint given one endpoint (-1,6) and the midpoint is (4,2)

Answer 1

The required points of the given line segment are ( 9, - 2 ).

Explanation:

Given that the line segment AB whose midpoint M is ( 4, 2 ) and point A is ( - 1, 6), 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 ( - 1, 6 ), B ( x, y ) with midpoint M ( 4, 2 ) -

then by the midpoint formula M are-

( 4, 2 ) = (
`( - 1 + x)/( 2)` ,
`( 6 + y)/(2)` )

On comparing x coordinate and y coordinate -

We get,

(
`( -1 + x)/(2)` = 4 ,
`( 6 + y)/(2)` = 2)

( - 1 + x = 8, 6 + y = 4)

( x = 8 + 1, y = 4 - 6 )

( x = 9, y = -2 )

Hence the required points A are ( 9, - 2 ).

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