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 ( ) and ( )then the mid points M are-
M = ( , )
Here,
Let A ( 2, - 13 ), B ( x, y ) with midpoint M ( - 4, - 10 ) -
then by the midpoint formula M are-
<em>( - 4, - 10 ) = ( , )</em>
On comparing x coordinate and y coordinate -
We get,
<em>( = - 4 , = - 10)</em>
<em>( x + 2 = - 8, - 13 + y = - 20 )</em>
<em>( x = - 8 - 2, y = - 20 + 13 )</em>
<em>( x = - 10, y = - 7 )</em>
Hence the required points A are ( - 10, - 7 ).
We can also verify by putting these points into Midpoint formula.