The midpoint of \overline{\text{AB}}
AB
is M(3, -2)M(3,−2). If the coordinates of AA are (8, 4)(8,4), what are the coordinates of BB?

Answers

Answer 1

Answer:

Step-by-step explanation: I am trying to interpret the question: I'll assume:

Line AB has a midpoint, M.

A is (8,4)

B is unknown, but desired

M is (3,-2)

We'll assume a straight line of the form y=mx+b, where m is the slope. m can be calculated by the "Rise" over the "Run" between the points A and M:

Rise = (4-(-2))=6

Run = (8-3)=5

Slope = (Rise/Run) = (6/5)

The line becomes y=(6/5)x+b

Calculate b, the y-intercept (the value of y when x is 0), by entering one of the two known points. I'll choose (8,4).

y=(6/5)x+b

4 = (6/5)(8)+b

b = 4 - (6/5)(8)

b = 4 - (48/5)

b = 4 - (9 3/5) or -5 3/5

The equation becomes:

y=(6/5)x - 5 3/5

Point B will have an x value of -2 [The change in x from A to M was (3-8) = -5. From M to 5 would be another -5 increment, so x goes from 3 to (3-5) or -2.

Find the value of y for x=-2:

y=(6/5)x - 5 3/5

y=(6/5)*(-2) - 5 3/5

y=(-12/5) - (28/5)

y = -(40/5) or - 8

B has coordinates of (-2, -8)

Answer 2

If coordinates of point A is (8, 4), then the coordinate of point B will be (-2, -8).

The "Midpoint-Formula" is used to find the coordinates of a point that lies exactly halfway between two given points. It's given as :Midpoint (M) = ((x₁ + x₂)/2, (y₁ + y₂)/2),

In this case, we have the midpoint as M(3, -2) and one of the endpoints as A(8, 4). We need to find coordinates of other endpoint which is B,

Using the midpoint formula, we rearrange it to solve for the missing coordinates (x₂, y₂),

x₂ = 2 × Mₓ - x₁,

y₂ = 2 × [tex]M_{y}[/tex] - y₁,

Substitute the given values:

We have : Mₓ = 3; [tex]M_{y}[/tex] = -2,

x₁ = 8; y₁ = 4

x₂ = 2 × 3 - 8 = -2;   y₂ = 2 × -2 - 4 = -8,

Therefore, the coordinates of point-B is(-2, -8).

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The given question is incomplete, the complete question is

The midpoint line AB is M(3, -2). If the coordinates of A is (8,4), What are the coordinates of B?


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