Answer: To find point Q on the line segment PR that partitions it into the segments PQ and QR in the ratio 4:5, we need to use the concept of proportion.
We can set up the proportion as:
PQ / QR = 4 / 5
To find the actual point Q on the line segment PR, we need to know the coordinates of points P and R. Without them, it is not possible to find the point Q. Once we have the coordinates of P and R, we can use the proportion above to find the coordinates of Q.
Alternatively, we can use the concept of a "partitioned ratio" which is a way to split a line segment into a certain ratio. It is found by adding the two ratios together and then dividing the length of the line segment by that number. In this case (4+5 =9) and then PQ = (4/9) * PR and QR = (5/9) * PR.
Explanation: