Question

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

Answer 1

Answer:

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

Step-by-step 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 = ( $\frac{ x_{1} + x_{2} }{2}$ , $\frac{ y_{1}  + y_{2}}{2}$   )

Here,

Let A ( - 1, 6 ), B ( x, y ) with midpoint M ( 4, 2 ) -

then by the midpoint formula M are-

( 4, 2 )  = ( $\frac{ - 1 + x}{ 2}$ ,  $\frac{ 6 + y}{2}$ )

On comparing x coordinate and y coordinate -

We get,

( $\frac{ -1 + x}{2}$ = 4 , $\frac{ 6 + y}{2}$  =  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.