To find the coordinates of point M, which lies on the segment with midpoint N, we can use the midpoint formula.
The midpoint formula states that the coordinates of the midpoint (M) between two points (P and N) can be found by taking the average of their respective x-coordinates and the average of their respective y-coordinates.
Given that the coordinates of P are (-3, 16) and the coordinates of N are (4, 10), we can apply the midpoint formula as follows:
1. Calculate the average of the x-coordinates:
x-coordinate of M = (x-coordinate of P + x-coordinate of N) / 2
x-coordinate of M = (-3 + 4) / 2 = 1 / 2 = 0.5
2. Calculate the average of the y-coordinates:
y-coordinate of M = (y-coordinate of P + y-coordinate of N) / 2
y-coordinate of M = (16 + 10) / 2 = 26 / 2 = 13
Therefore, the coordinates of point M are (0.5, 13).