Question

The midpoint of \overline{\text{AB}}AB is M(-2, 1)M(−2,1). If the coordinates of AA are (1, -2)(1,−2), what are the coordinates of BB?​

Answer 1

Answer:

B=(-5, 4)

The coordinates of BB are (-5, 4)(-5,4)

Step-by-step explanation:

To solve, we will follow the steps below;

mid point = m(-2,1)

coordinates A is (1,-2)

To find the coordinates B

We will use the formula

($x_{m}$,$y_{m}$) = ($x_{1}$ + $x_{2}$ /2  ,      $y_{1}$ +$y_{2}$/2)

from the question

($x_{m}$,$y_{m}$)  = (-2,1)    

this implies

$x_{m}$ = -2    $y_{m}$ = 1

Also

A($x_{1}$ , $y_{1}$)           B( $x_{2}$ ,$y_{2}$)

A(1, -2)           B( $x_{2}$ ,$y_{2}$)

$x_{1}$= 1     $y_{1}$ =-2

we are to look for  $x_{2}$    and $y_{2}$

$x_{m}$ = $x_{1}$ + $x_{2}$ /2

-2 = 1 + $x_{2}$ /2

multiply both-side by 2

-4 = 1+ $x_{2}$

subtract 1 from both-side of the equation

-4-1 =$x_{2}$

-5 = $x_{2}$

$x_{2}$ = -5

Similarly,

$y_{m}$ =   $y_{1}$ +$y_{2}$/2

 1 =   -2+$y_{2}$/2

multiply both-side of the equation  by 2

2 =   -2 +$y_{2}$

add 2 to both-side of the equation

2+2 = -2+ 2 +$y_{2}$

 4=$y_{2}$

 $y_{2}$  = 4

The coordinates of BB are (-5, 4)(-5,4)