Answer:
k = -9.
Step-by-step explanation:
As the triangle is right-angled at Q, by Pythagoras:
PR^2 = PQ^2 + RQ^2
So, substituting the given data and using the distance formula between 2 points:
(7 - 1)^2 + (k - 4)^2 = (-4-4)^2 + (-3-1)^2 + (7 - (-3))^2 + (k - (-4))^2
36 + (k - 4)^2 = 64 + 16 + 100 + ( k + 4)^2
(k - 4)^2 - (k + 4)^2 = 180 - 36
k^2 - 8k + 16 - (k^2 + 8k + 16) = 144
-16k = 144
k = -9.
Hello here is a solution :
Answer:
y = 3/2 * x + 12
Step-by-step explanati
2x + 3y = 12
y = -2/3x + 4
slope: -2/3
slope' of perpendicular line: 3/2
6 = 3/2 * (-4) + b
b = 12
equation: y = 3/2 * x + 12
