Final answer:
The student is looking to find the point q on a line segment, with given points p and p0. By applying the ratio formula and solving for each coordinate, it is determined that the point q is (38, 19, 59).
Step-by-step explanation:
The student is asking how to find a point q that lies on the line segment between two given points p and p0, where p0 is 1/8 of the way from p to q. To solve this, use the following formula for any point R that divides the segment between two points A (x1, y1, z1) and B (x2, y2, z2) in a ratio of 1:n:
- xR = (x1 + n*x2)/(1 + n)
- yR = (y1 + n*y2)/(1 + n)
- zR = (z1 + n*z2)/(1 + n)
In this case, A is point p (-2, 3, -5), point R is p0 (3, 5, 3) and the ratio 1:n is 1:7, since p0 is 1/8th of the way from p to q.
Solve for x, y, z components of q separately:
- xq = (1 + 7)*3 - 7*(-2) = 3 + 21 + 14 = 38
- yq = (1 + 7)*5 - 7*(3) = 5 + 35 - 21 = 19
- zq = (1 + 7)*3 - 7*(-5) = 3 + 21 + 35 = 59
Therefore, the point q is (38, 19, 59).