Suppose the coordinate of P is 2, PQ = 8, and PR = 12. What are the possible coordinates of the midpoint of the given segment? The coordinates are PQ, PR, and QR.
(2,4)
To find the possible coordinates of the midpoint of segment PQ, we need to first find the coordinates of point Q and R.
Given that the coordinate of point P is 2, we know that point Q lies 8 units to the right of point P on the x-axis. Therefore, the x-coordinate of point Q can be found by adding 8 to the x-coordinate of point P:
x-coordinate of Q = x-coordinate of P + PQ
x-coordinate of Q = 2 + 8
x-coordinate of Q = 10
Next, we need to find the y-coordinate of Q. Since the segment PQ is horizontal, the y-coordinate of point Q will be the same as the y-coordinate of point P. Therefore, the y-coordinate of point Q is:
y-coordinate of Q = y-coordinate of P
(Note: The y-coordinate of P has not been given. It is missing in the information you provided.)
Similarly, to find the coordinates of point R, we know that point R lies 12 units to the right of point P on the x-axis. Thus:
x-coordinate of R = x-coordinate of P + PR
x-coordinate of R = 2 + 12
x-coordinate of R = 14
Again, we need to find the y-coordinate of R. Since the segment PR is horizontal, the y-coordinate of point R will be the same as the y-coordinate of point P.
Now that we have the coordinates of points Q and R, we can find the midpoint of segment PQ by taking the average of their x-coordinates and y-coordinates.
x-coordinate of midpoint (M) = (x-coordinate of Q + x-coordinate of R) / 2
y-coordinate of midpoint (M) = (y-coordinate of Q + y-coordinate of R) / 2
Substituting the coordinates of Q and R:
x-coordinate of M = (10 + 14) / 2
x-coordinate of M = 24 / 2
x-coordinate of M = 12
y-coordinate of M = (y-coordinate of Q + y-coordinate of R) / 2
(Note: The y-coordinate of Q and R are the same, which is the y-coordinate of P.)
Therefore, the possible coordinates of the midpoint of the given segment PQ can be (12, y), where y is the y-coordinate of point P. However, since the y-coordinate of point P is missing in the given information, we cannot determine the exact coordinates of the midpoint unless the y-coordinate of point P is provided.