A line passes through A(2,3) and B(5,7). Find: (a) The coordinates of the point P on AB extended through B to P so that P is twice as far from A as from B; (b) the coordinates if P is on AB extended through A so that P is twice as far from B as from A.
Division of Line Segments (Locating a Point)
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algebraic-geometry
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0Where are you getting stuck? Please include everything you have tried so far. – 2017-01-26
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0I got 2 terminal points which has coordinates (a)P(8,11) and (b)P(0.5,1). – 2017-01-26
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0as I graph it. It doesnt seem like it concide with the given problems. I use an equation x=x1+r(x2-x1) – 2017-01-26
1 Answers
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Equation of your line is $y=\frac{1}{3}+\frac{4}{3}x$, which you can derive by solving $3=a+2b$ and $7=a+5b$. A point on the line twice as far from A than from B will have $x=5+(5-2)$. A point on the line twice as far from B than from A will have $x=2-(5-2)$.
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0Pardon me good sir. I am quite confuse about the equation line. – 2017-01-26
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0A line passing through your $A$ and $B$ points is a collection of points $(y,x)$, where $y=1/3+4/3\cdot x$. – 2017-01-26