+39 Points A, B, and c are given in the coordinate plane. There exists a point Q and a constant k such that for any point P,
PA^2 + PB^2+PC^2=3PQ^2 + k
If A = (4, -4), B = (3, 5), and C = (-1, 2), then find the constant k.
+128570 Here's a similar problem
https://web2.0calc.com/questions/pls-help-asap_78#r1
See if you can take it from here
If not, let me know and I'll help you
+128570 Let P = (x,y)
PA^2 + PB^2 + PC^2 =
(x - 4)^2 + ( y + 4)^2 + ( x - 3)^2 + ( y -5)^2 + (x + 1)^2 + (y-2)^2
Simplifying this we get
3 x^2 - 12 x + 3 y^2 - 6 y + 71
3 [ x^2 - 4x + y^2 - 2y ] + 71 complete the square on x, y
3 [ x^2 -4x + 4 + y^2 -2y + 1 ] + 71 - 12 - 3
3 [ ( x - 2)^2 + (y - 1]^2 ] + 56
Q = (2, 1)
k = 56
CORRECTED
