The coordinates of point Q, dividing the segment PR in the ratio 5:1, can be calculated using the section formula, taking the weighted average of the coordinates of P and R.
To find the coordinates of point Q that lies on the line segment PR such that the ratio of PQ to QR is 5:1, we can utilize the concept of section formula or internal division. If we assume that P(x1, y1) and R(x2, y2) are the coordinates of points P and R, then the coordinates of point Q can be found using the formula:
Q(x, y) = ((mx2 + nx1) / (m+n), (my2 + ny1) / (m+n))
Where m:n represents the given ratio. Substituting m = 5 and n = 1 gives us the final coordinates of Q. This method works because it finds a weighted average of the coordinates, taking into account the given ratio.
Therefore, answer will be in the form:
Q(x, y) = ((5x2 + x1) / 6, (5y2 + y1) / 6)
This equation gives us the coordinates of the point Q that divides the segment PR in the ratio of 5:1.