Final answer:
Using the midpoint formula, the given midpoint is calculated as the average of the coordinates of endpoints P1 and P2. By substituting the midpoint (-8,5) and given point P1 (-9,6), the coordinates of P2 are determined to be (-7,4).
Step-by-step explanation:
To determine the coordinates of the second point P2, we use the property that the midpoint of a line segment is the average of the coordinates of the endpoints. Given the midpoint is at (-8, 5) and one endpoint P1 is at (-9, 6), we can set up equations to solve for the unknown coordinates of P2 (x2, y2).
The formula for the midpoint (xm, ym) is given by:
xm = (x1 + x2) / 2
ym = (y1 + y2) / 2
Substituting the known values, we get:
-8 = (-9 + x2) / 2
5 = (6 + y2) / 2
From these equations, we can solve for x2 and y2:
x2 = -8 * 2 + 9 = -7
y2 = 5 * 2 - 6 = 4
Thus, the coordinates of P2 are (-7, 4).