Let P 1 3 7 If the point 4 0 6 is the midpoint of the line

Let P = (1, 3, 7). If the point (4, 0, -6) is the midpoint of the line segment connecting P and Q, what is Q?

Solution

P = (1, 3, 7). point (4, 0, -6) is the midpoint of the line segment connecting P and Q

let Q=(x,y,z)

(4, 0, -6)=[P+Q]/2

(4, 0, -6)=[(1, 3, 7)+(x,y,z)]/2

(4*2, 0*2, -6*2)=[(1+x, 3+y, 7+z) ]

(8,0,-12)=(1+x, 3+y, 7+z)

(1+x, 3+y, 7+z)=(8,0,-12)

1+x =8 ==>x =7

3+y =0 ==>y =-3

7+z =-12 ==> z =-19

Q=(x,y,z)=(7,-3,-19)