Question

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

Answer 1

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

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=((x_1+x_2)/(2),(y_1+y_2)/(2))`

Midpoint of A and B is

`Midpoint=((4+a)/(2),(-5+b)/(2))`

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

`(-2,10)=((4+a)/(2),(-5+b)/(2))`

On comparing both sides we get

`-2=(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=(-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).