The line joining the points A-3-10 and B-2-6 is divided by the point P such that PBAB-15- find the co-ordinate of P-

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Standard X

Mathematics

Section Formula

The line join...

Question

The line joining the points $A (- 3, - 10)$ and $B (- 2, 6)$ is divided by the point $P$ such that $\frac{P B}{A B} = \frac{1}{5}$ , find the co-ordinate of $P$ .

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Solution

Using the section formula, if a point $(x, y)$ divides the line joining the points $(x_{1}, y_{1})$ and $(x_{2}, y_{2})$ in the ratio $m : n$ , then
$(x, y) = (\frac{m x_{2} + n x_{1}}{m + n}, \frac{m y_{2} + n y_{1}}{m + n})$
Given $P B : A B = 1 : 5$
$∴$ $P B : P A = 1 : 4$
Coordinates of $P$ are
$(x, y) = (\frac{4 \times (- 2) + 1 \times (- 3)}{5}, \frac{4 \times 6 + 1 \times (- 10)}{5})$
$= (- \frac{11}{5}, \frac{14}{5})$

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The line joining the points A(−3,−10) and B(−2,6) is divided by the point P such that PBAB=15, find the co-ordinate of P.

Using the section formula, if a point (x,y) divides the line joining the points (x1,y1) and (x2,y2) in the ratio m:n, then (x,y)=(mx2+nx1m+n,my2+ny1m+n)Given PB:AB=1:5∴ PB:PA=1:4Coordinates of P are(x,y)=(4×(−2)+1×(−3)5,4×6+1×(−10)5)=(−115,145)

The line joining the points $A (- 3, - 10)$ and $B (- 2, 6)$ is divided by the point $P$ such that $\frac{P B}{A B} = \frac{1}{5}$ , find the co-ordinate of $P$ .