Question

Find the coordinates of the other endpoint of the​ segment, given its midpoint and one endpoint.​ (Hint: Let​ (x,y) be the unknown endpoint. Apply the midpoint​ formula, and solve the two equations for x and​ y.)
midpoint ​( -4−10​), endpoint ​(2.−13​)

Answer 1

Answer:

The required points of the given line segment  are ( - 10, - 7 ).

Step-by-step explanation:

Given that the line segment AB whose midpoint M is ( - 4, -10 ) and point A is ( 2, - 13), 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 ( 2, - 13 ), B ( x, y ) with midpoint M ( - 4, - 10 ) -

then by the midpoint formula M are-

( - 4, - 10 )  = ( $\frac{ 2 + x}{2}$ , $\frac{- 13 + y}{2}$ )

On comparing x coordinate and y coordinate -

We get,

( $\frac{x + 2}{2}$ = - 4  ,  $\frac{ - 13 + y}{2}$ = - 10)

( x + 2 = - 8, - 13 + y = - 20 )

( x = - 8 - 2, y = - 20 + 13 )

( x = - 10, y = - 7 )

Hence the required points  A are ( - 10, - 7 ).

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