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?

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erinna erinna · Answer 1 · 2019-12-27T11:17:59+01:00

Answer:

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

Step-by-step 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

[tex]Midpoint=(\dfrac{x_1+x_2}{2},\dfrac{y_1+y_2}{2})[/tex]

[tex]M=(\dfrac{-4+a}{2},\dfrac{8+b}{2})[/tex]

Coordinates of midpoint are (1,7.5).

[tex](1,7.5)=(\dfrac{-4+a}{2},\dfrac{8+b}{2})[/tex]

On comparing both sides we get

[tex]1=\dfrac{-4+a}{2}\Rightarrow 2=-4+a\Rightarrow a=6[/tex]

[tex]7.5=\dfrac{8+b}{2}\Rightarrow 15=8+b\Rightarrow b=7[/tex]

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