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Let point A be (2,7) and point B be (6, 8). What point is on the segment connecting A and B such that the distance from the point to B is 5 times the distance from the point to A?

 Nov 15, 2022
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Point C

 

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\({\color{blue}m}=\frac{y_B-y_A}{x_B-x_A}=\frac{8-7}{6-2}=\color{blue}\frac{1}{4}\\ y=m(x-x_A)+y_A=\frac{1}{4}(x-2)+7\\ \color{blue}y=\frac{1}{4}x+7.5\)

\(\Delta x=\frac{x_B-x_A}{6}=\frac{6-2}{6}=\frac{2}{3}\\ {\color{blue}x_C=}\ x_A+\Delta x=\color{blue}2\frac{2}{3}\\ y_C=\frac{1}{4}(x-2)+7\\ \color{blue}y_C=7.1\overline 6=\frac{43}{6}\)

 

Point \(C\ (2\frac{2}{3},7\frac{1}{6})\) is on the segment connecting A and B such that the distance from the point C to B is 5 times the distance from the point C to A.

laugh  !

 Nov 15, 2022
edited by asinus  Nov 15, 2022

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