Question

M(3,2) is the midpoint of segment AB. B(-2,5). What are the coordinates of A

Answer 1

Answer:

The required points of the given line segment  are ( 8, -1 ).

Step-by-step explanation:

Given that the line segment AB whose midpoint M is ( 3, 2 ) and point B is ( -2, 5), then we have to find point A 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 C are-  

C = ( $\frac{x_{1} + x_{2} }{2}$ , $\frac{ y_{1} + y_{2}} {2}$ )

Here,

Let A ( x, y ), B ( -2, 5 ) with midpoint M ( 3, 2 )-

then by the midpoint formula C are-

( 3, 2 )  = ( $\frac{x - 2}{2}$  ,  $\frac{ y + 5}{2}$ )

On comparing x coordinate and y coordinate -

We get,

( $\frac{x - 2}{2}$ = 3  , $\frac{y + 5}{2}$ = 2)

( x - 2 = 6, y + 5 = 4 )

( x = 6 + 2, y = 4 - 5 )

( x = 8, y = -1 )

Hence the required points  A are (8, -1 ).

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