Question

The midpoint of segment AB is (4, 2). The coordinates of point A are (2, 7). Find the coordinates of point B.

Answer 1

Answer:

The option B) is correct

Therefore the coordinate of B$(x_2,y_2)$ is (6,-3)

Step-by-step explanation:

Given that the midpoint of segment AB is (4, 2). The coordinates of point A is (2, 7).

To Find the coordinates of point B:

• Let the coordinate of A be $(x_1,y_1)$ is (2,7) respectively
• Let the coordinate of B be $(x_2,y_2)$
• And Let M(x,y) be the mid point of line segment AB is (4,2) respectively
• The mid-point formula is

$M(x,y)=(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})$

• Now substitute the coordinates int he above formula we get
• $(4,2)=(\frac{2+x_2}{2},\frac{7+y_2}{2})$
• Now equating we get

$4=\frac{2+x_2}{2}$                    $2=\frac{7+y_2}{2}$

Multiply by 2 we get                             Multiply by 2 we get  

$4(2)=2+x_2$                                           $2(2)=7+y_2$

$8=2+x_2$                                                $4=7+y_2$

Subtracting 2 on both

the sides                                    Subtracting 7 on both the sides

$8-2=2+x_2-2$                                $4-7=7+y_2-7$

$6=x_2$                                                       $-3=y_2$

Rewritting the above equation      Rewritting the equation

$x_2=6$                                                      $y_2=-3$

Therefore the coordinate of B$(x_2,y_2)$ is (6,-3)

Therefore the option B) is correct.