Respuesta :
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:
[tex]Midpoint=(\dfrac{x_1+x_2}{2},\dfrac{y_1+y_2}{2})[/tex]
Midpoint of A and B is
[tex]Midpoint=(\dfrac{4+a}{2},\dfrac{-5+b}{2})[/tex]
It is given that M(−2, 10) is the midpoint of AB.
[tex](-2,10)=(\dfrac{4+a}{2},\dfrac{-5+b}{2})[/tex]
On comparing both sides we get
[tex]-2=\dfrac{4+a}{2}[/tex]
Multiply both sides by 2.
[tex]-4=4+a[/tex]
Subtract 4 from both sides.
[tex]-8=a[/tex]
The value of a is 8.
Similarly,
[tex]10=\dfrac{-5+b}{2}[/tex]
Multiply both sides by 2.
[tex]20=-5+b[/tex]
Add 5 on both sides.
[tex]25=b[/tex]
Therefore, the coordinates of B are (-8,25).
