Answer:
(-14,12)
Explanation:
Way 1: (little more complicated)
we know two things,
The two halves of the line have the same slope, and that the length from the endpoint to the midpoint is equal to the length from the midpoint to the other end point.
The slope is equal to: (6-9)/(4-(-5)) = -3/9 = -1/3
The length is equal to (using the Pythagorean theorem):
height = delta y = 9 - 6 = 3
length = delta x = 4 - (-5) = 9
3^2+9^2=hypotenuse^2
9+81 = h^2
h = sqrt(90)
So, the let's say point Q has the coordinate (a, b).
The formula of the slope would give us (b-9)/(a-(-5)) = -1/3
The formula of the hypotenuse would give us (b-9)^2+(a-(-5))^2 = 90
solving the system of equations, we would get that a = -14 and b = 12, so the point is (-14,12)
Make sure to be careful, however, because you will get two points with this system of equations. Only one works
Way 2:
since from point P to the midpoint we went to the left by 9 and up by 3, from the midpoint to point Q, we would go left by 9, and up by 3.
from the midpoint (-5,9), go left by 9, so x decreases by 9 to get (-14, 9).
go up by 3, so y increases by 3 to get (-14,12). This agrees with our other answer