Question

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

Answer 1

Answer:

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

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

Here,

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

then by the midpoint formula M are-

( 3, - 2 )  = ( $\frac{ 7 + x}{2}$ , $\frac{ - 9 + y}{2}$ )

On comparing x coordinate and y coordinate -

We get,

( $\frac{ 7 + x}{2}$ = 3  , $\frac{ - 9 + y}{2}$  = - 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.