Question

Point A is at (-7,-7) and point M is at (-6,-1). Point M is the midpoint of point A and B. What are the coordinates of point B?

Answer 1

Answer:

(-5,5)

Step-by-step explanation:

For point (x1,y1) and (x2,y2) on a coordinate plane ,

coordinate of midpoint is given by (x1+x2)/2, (y1+y2)/2

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In the problem

point A(-7,-7)

let point B be (x,y) thus

midpoint point M for AB will be (-7+x)/2, (-7+y)/2

It is given that M is(-6,-1)

hence  (-7+x)/2, (-7+y)/2 will be same as (-6,-1)

Thus,

(-7+x)/2 = -6            and  (-7+y)/2 = -1

=> -7+x = -6*2                =>  -7+y = -1*2

=> -7+x = -12                  => -7+y = -2

=> x = -12+7                   => y = -2+7

=> x = -5                        => y = 5

Thus, coordinates of point B is (x,y) = (-5,5)

Answer 2

The coordinates of point B are (-5, 5).

Given that,

Point A is at (-7,-7), and points M is at (-6,-1).

Point M is the midpoint of points A and B.

We have to determine,

What are the coordinates of point B?

According to the question,

Point A $(x_1, y_1)$ and point B $(x_2, y_2)$ be the ending point of the line segment.

The midpoint formula of a line segment joining these two points is given as:

$\rm Midpoint \ of \ point \ (A, \ B) = \left( \dfrac{x_1+y_1}{2} , \ \dfrac{x_2+y_2}{2} \right )$

Then,

Let the coordinates of point B be (x, y),

Point A is at (-7,-7), and points M is at (-6,-1).

Point M is the midpoint of points A and B.

Therefore,

The coordinates of point B is,

$\rm y_1 = \dfrac{x_1+x}{2} \\\\-6 = \dfrac{-7+x}{2} \\\\-6 \times 2= -7 + x\\\\-12 = -7 + x \\\\ x= -7+12\\\\ x = -5$

And,

$\rm y_2 = \dfrac{x_2+y}{2} \\\\-1 = \dfrac{-7+y}{2} \\\\-1 \times 2= -7 + y\\\\-2 = -7 +y_2 \\\\y= 7-2\\\\y = 5$

Hence, The coordinates of point B are (-5, 5).

For more details refer to the link given below.

https://brainly.com/question/15161263