The line joining the points A - 3 - - 10 and A - 2-6 divided by the point P such that P B A B - 1 5 - Find the co-ordinates of P-

A( 3, 10) B( 2,6) PB AB = 1 5 5PB=AB 5(AB AP)=AB 5AB AB=5AP 4AB=5AP AP AB = 4 5 AP AB ÷ PB AB = 4 5 ÷ 1 ...

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Standard X

Mathematics

Distance Formula

The line join...

Question

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

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Solution

$A (- 3, - 10) B (- 2, 6) \frac{P B}{A B} = \frac{1}{5} 5 P B = A B 5 (A B - A P) = A B 5 A B - A B = 5 A P 4 A B = 5 A P \frac{A P}{A B} = \frac{4}{5} \frac{A P}{A B} \div \frac{P B}{A B} = \frac{4}{5} \div \frac{1}{5} \Rightarrow \frac{A P}{P B} = \frac{4}{1}$
ratio in which $P$ divides $A B = 4 : 1$
$m : n = 4 : 1$
$x = \frac{m x_{2} + n x_{1}}{m + n} \Rightarrow x = \frac{4 \times - 2 + 1 \times - 3}{5} = \frac{- 8 - 3}{5} = \frac{- 11}{5} y = \frac{m y_{2} + n y_{1}}{m + n} y = \frac{4 \times 6 + 1 \times - 10}{5} = \frac{24 - 10}{5} = \frac{14}{5}$
$∴$ Co-ordinate of $P = (\frac{- 11}{5}, \frac{14}{5})$

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Q. a) Find the ratio in which the point P (-1, a) divides the joining of points A(-5, 4) and B (3, -2). Hence, find a.

b)
The line joining the points A(4, -5) and B (4, 5) is divided by the point P, such that AP: PB = 2 : 3. Find the coordinates of point P.

[6 MARKS]

P

is a point on the line joining

A (4, 3)

and

B (- 2, 6)

such that

5 A P = 2 B P

. Find the coordinates of

P

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

A(−3,−10)B(−2,6)PBAB=155PB=AB5(AB−AP)=AB5AB−AB=5AP4AB=5APAPAB=45APAB÷PBAB=45÷15⇒APPB=41ratio in which P divides AB=4:1m:n=4:1x=mx2+nx1m+n⇒x=4×−2+1×−35=−8−35=−115y=my2+ny1m+ny=4×6+1×−105=24−105=145∴ Co-ordinate of P=(−115,145)

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