The midpoint of AB is M(0, -4). If the coordinates of A are (-8, -7), what are the coordinates of B?

Question

this is my geometry classwork, need help asap

Answer 1

Try to think of this conceptually. AB indicates a line segment, but the important part is that it is straight. The midpoint, by definition, divides this line segment in half, so the direction of trajectory remains the same in the missing part, and the length of the known half is the same as the length of the unknown half. This can be figured out by simply drawing the line segment on graph paper, or you can use the so-called midpoint formula: M=[(x1+x2)/2], [(y1+y2)/2]. However, we must manipulate this formula because we already know the midpoint and we do not know (x2, y2).

Let's give it a try:

We write known information into the formula: (0,-4)=[(-8+x2)/2], [(-7+y2)/2]

Now notice the x1, x2, y1, and y2. We can now separate these into two equations, one for x and one for y:

0=(-8+x2)/2

-4=(-7+y2)/2

Now use basic algebra to get rid of the "divided by two" (/2) by multiplying each side by two:

0x2=-8+x2

-4x2=-7+y2

Now combine/resolve like terms:

0=-8+x2

-8=-7+y2

Now solve the equations:

x2=8

y2=-1

Thus, B=(8,-1)

Again, think of this conceptually: the midpoint between -8 and 8 is zero, and the midpoint between -7 and -1 is -4. Doing it both ways, and arriving at the same result virtually guarantees you have the correct answer!

Answer 2

Locate the Mid-Point Formula

(x_A + x_B) / 2 = x_M

(-8 + x_B) / 2 = 0

-8 + x_B = 0

x_B = 8

Do the same for y_A, y_B, and y_M

Answer 3

1) With any math question, we first need to find the right formula. In this case it is the midpoint formula. If you're not sure, just type into a search engine; "Formula for midpoints in geometry" you should find this very quickly.

2) Write down the formula:

(X1+X2)/2 = Xm, (Y1+Y2)/2 = Ym

3) Substitute what is given into the formula:

(-8+X)/2=0, (-7+Y)/2=-4

4) Solve for X and Y (first multiply both sides of equation by 2)

-8+x=0

X = 8

-7+Y=-8

Y = -1

5) Write down final answer;

B (8,-1)