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

User Stepan Maksymov
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1 Answer

19 votes
19 votes

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)

User Matt Murrell
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