Question

????(−2, 10) is the midpoint of . If ???????? has coordinates (4, −5), what are the coordinates of ?????

Answer 1

Answer:

The coordinates of B are (-8,25).

Step-by-step explanation:

Consider the completer question is " M(−2, 10) is the midpoint of AB. If A has coordinates (4, −5), what are the coordinates of B".

Let coordinates of B are (a,b).

Formula for midpoint:

$Midpoint=(\dfrac{x_1+x_2}{2},\dfrac{y_1+y_2}{2})$

Midpoint of A and B is

$Midpoint=(\dfrac{4+a}{2},\dfrac{-5+b}{2})$

It is given that M(−2, 10) is the midpoint of AB.

$(-2,10)=(\dfrac{4+a}{2},\dfrac{-5+b}{2})$

On comparing both sides we get

$-2=\dfrac{4+a}{2}$

Multiply both sides by 2.

$-4=4+a$

Subtract 4 from both sides.

$-8=a$

The value of a is 8.

Similarly,

$10=\dfrac{-5+b}{2}$

Multiply both sides by 2.

$20=-5+b$

Add 5 on both sides.

$25=b$

Therefore, the coordinates of B are (-8,25).