Question

The point Q lies on the segment PR. Find the coordinates of Q so that PQ is 3/5 of PR.

P=(-1,4)
R=(14,-21)

Answer 1

To find the coordinates of point Q which divides segment PR in a ratio such that PQ is 3/5 of PR, we use the section formula with P=(-1,4) and R=(14,-21), resulting in Q's coordinates being (8, -11).

Step-by-step explanation:

The student is asking how to find the coordinates of point Q that divides the line segment PR in a specific ratio, where P=(-1,4) and R=(14,-21), and PQ is 3/5 of PR. We can use the section formula, which states that if a point Q divides a segment PR in the ratio m:n, then the coordinates of Q are given by ((mx2 + nx1)/(m+n), (my2 + ny1)/(m+n)). In this case, m=3 and n=2. Thus, the coordinates of Q can be calculated as follows:

1. Find the x-coordinate of Q: ((3*14) + (2*-1))/(3+2) = (42 - 2) / 5 = 40 / 5 = 8.
2. Find the y-coordinate of Q: ((3*-21) + (2*4))/(3+2) = (-63 + 8) / 5 = -55 / 5 = -11.

Therefore, the coordinates of point Q are (8, -11).