Question

If (3, 10) is the endpoint of a line segment, and
(-2, 3) is its midpoint, find the other endpoint.

Answer 1

Answer:

The required points of the given line segment  are ( - 7, - 4 ).

Step-by-step explanation:

Given that the line segment AB whose midpoint M is ( - 2, 3 ) and point A is ( 3, 10), 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 ( 3, 10 ), B ( x, y ) with midpoint M ( - 2, 3 ) -

then by the midpoint formula M are-

( - 2, 3 )  = ( $\frac{ 3 + x}{2}$ , $\frac{ 10 + y}{2}$ )

On comparing x coordinate and y coordinate -

We get,

( $\frac{ 3 + x}{2}$ = - 2  , $\frac{ 10 + y}{2}$ = 3)

( 3 + x = - 4, 10 + y = 6 )

( x = - 4 - 3, y = 6 - 10 )

( x = - 7, y = -4 )

Hence the required points  A are ( - 7, - 4 ).

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