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Given a point P(8,1) on Segment AB with A(-2,3), find the coordinates of B if AP/AB= 2/3

 Sep 20, 2020
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Given a point P(8,1) on Segment AB with A(-2,3), find the coordinates of B if AP/AB= 2/3

 

Hello Guest!

 

\(m={\color{black}\frac{y_P-y_A}{x_P-x_A}=-\frac{2}{10}=-}0.2\)

\(f(x)=m(x-x_P)+y_P\)

\(f(x)=-0.2(x-8)+1\)

\(f(x)=-0.2x+2.6\)

 

\(\color{blue}(x_P-x_A):(x_B-x_A)=2:3\\ 2x_B-2x_A=3x_P-3x_A\\ 2x_B=3x_P-3x_A+2x_A\\ 2x_B=3\cdot 8-3\cdot (-2)+2\cdot (-2)\\ x_B=12+3-2\)

\(x_B=13\)

\(y_B=-0.2\cdot 13+2.6\)

\(y_B=0\)

 

The coordinates of B: \( B\ (13,0)\)

laugh  !

 Sep 20, 2020
edited by asinus  Sep 21, 2020

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