Question

Find point P such that the segment with endpoints A (2, 4) and B (17, 14) in a ratio of 2:3P: ( , )

Answer 1

We are given the following endpoints

A (2, 4) and B (17, 14)

We need to find point P such that the segment is in the rato of 2:3

Total segments = 2+3 = 5

The x-coordinate of the point P is given by

`\begin{gathered} x_p=x_1+(2)/(5)(x_2-x_1) \\ x_p=2_{}+(2)/(5)(17-2) \\ x_p=2_{}+(2)/(5)(15) \\ x_p=2_{}+6 \\ x_p=8 \end{gathered}`

The y-coordinate of the point P is given by

`\begin{gathered} y_p=y_1+(2)/(5)(y_2-y_1) \\ y_p=4+(2)/(5)(14-4) \\ y_p=4+(2)/(5)(10) \\ y_p=4+4 \\ y_p=8 \end{gathered}`

Therefore, the point P is (8, 8)