Question

Point \blue{A}Astart color blue, A, end color blue is at \blue{(-4, 8)}(−4,8)start color blue, left parenthesis, minus, 4, comma, 8, right parenthesis, end color blue and point \purple{M}Mstart color purple, M, end color purple is at \purple{(1, 7.5)}(1,7.5)start color purple, left parenthesis, 1, comma, 7, point, 5, right parenthesis, end color purple. Point \purple{M}Mstart color purple, M, end color purple is the midpoint of point \blue{A}Astart color blue, A, end color blue and point \green{B}Bstart color green, B, end color green. What are the coordinates of point \green{B}Bstart color green, B, end color green?

Answer 1

The coordinates of point B are (6,7).

Explanation:

Given points are

Blue = A(-4,8)

Purple = M(1,7.5)

Green = B

It is given that point M is the midpoint of point A and B.

Let coordinates of points are (a,b).

Midpoint of two points is

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

`M=((-4+a)/(2),(8+b)/(2))`

Coordinates of midpoint are (1,7.5).

`(1,7.5)=((-4+a)/(2),(8+b)/(2))`

On comparing both sides we get

`1=(-4+a)/(2)\Rightarrow 2=-4+a\Rightarrow a=6`

`7.5=(8+b)/(2)\Rightarrow 15=8+b\Rightarrow b=7`

Therefore, the coordinates of point B are (6,7).