W, R, and S are points on a number line, and W is the midpoint of point RS. For each pair of coordinates given, find the coordinate of the third point. Please correct me if I'm wrong!

1. R=4, S=-6
Answer: W=-1

2. W=-4, S=2
Answer: R=-10

*Could you please explain how you solve and get these two answers? Thanks!

the midpoint is the "average" of the two values

so for the 1st:
(4 + (-6))/2 = -2/2 = -1

in the second, you are given the "average"
let one of the endpoints be x

so (2+x)/2 = -4
multiply by 2
2+x = -8
x = -10

Verify you answer by drawing a number line, putting in the values you found or those that were give and

"count"

Sure! To find the coordinate of the third point, we can use the midpoint formula.

The midpoint formula states that the coordinate of the midpoint (W) is equal to the average of the coordinates of the two endpoints (R and S).

Let's calculate the coordinates of the third point in each given pair:

1. R = 4, S = -6
To find W, we calculate the average of R and S:
W = (R + S) / 2 = (4 + (-6)) / 2 = -2 / 2 = -1
So the coordinate of the third point W is -1.

2. W = -4, S = 2
Again, we calculate the average of W and S to find R:
R = (W + S) / 2 = (-4 + 2) / 2 = -2 / 2 = -1
So the coordinate of the third point R is -1.

Thus, in both cases, the coordinate of the third point is -1.

To find the coordinate of the third point given that W is the midpoint of points R and S, you can use the formula for the midpoint:

Midpoint = (Coordinate of R + Coordinate of S) / 2

Let's go through each problem step by step:

1. R = 4, S = -6
To find the coordinate of W, we use the midpoint formula:

W = (R + S) / 2
= (4 + (-6)) / 2
= (-2) / 2
= -1

So the coordinate for W is -1.

2. W = -4, S = 2
Again, we use the midpoint formula to find the coordinate of R:

R = 2 * W - S
= 2 * (-4) - 2
= -8 - 2
= -10

Therefore, the coordinate for R is -10.

In both cases, you correctly obtained the coordinates of W and R. Well done!