M is the midpoint of line segment AB.Find the missing coordinate for each
10a. A:p-4
M:8
B:p+12
must use ruler postulat
To find the missing coordinate, we need to use the midpoint formula. According to the Midpoint Formula, the x-coordinate of the midpoint is equal to the average of the x-coordinates of the two endpoints, and the same goes for the y-coordinate.
Here, we already have the x-coordinate of the midpoint, which is 8. We need to find the y-coordinate for each endpoint, A and B.
Let's start with the coordinate for point A. The x-coordinate for A is given as p - 4. However, we need to find the y-coordinate.
Since M is the midpoint of segment AB, the x-coordinate for A plus the x-coordinate for B must be equal to twice the x-coordinate for M.
So, we have:
(p - 4) + (p + 12) = 2 * 8
Simplifying the equation, we get:
2p + 8 = 16
Subtracting 8 from both sides, we have:
2p = 8
Dividing both sides by 2, we get:
p = 4
Now that we know the value of p, we can substitute it back into the x-coordinate for A, which is p - 4. So, substituting p = 4, we have:
x-coordinate of A = 4 - 4 = 0
Now, for the y-coordinate of B, we know the x-coordinate of B is p + 12, and since the x-coordinate of M is 8, we can set up another equation:
(p + 12) + 8 = 2 * 8
Simplifying the equation, we get:
p + 20 = 16
Subtracting 20 from both sides, we have:
p = -4
Now that we know the value of p, we can substitute it into the x-coordinate for B, which is p + 12. Substituting p = -4, we have:
x-coordinate of B = -4 + 12 = 8
Therefore, the missing coordinates for each endpoint are:
A: (0, missing)
B: (8, missing)