Question

If p divides the line segment dividing A(-2,3) and B(-4,0) such that Ap/AB = 2/5 find coordinates of P

Answer 1

$\bf{\Huge{\boxed{\sf{\green{ANSWER\::}}}}}$

$\bf{\Large{\underline{\bf{Given\::}}}}$

If P divides the line segment dividing A(-2,3) & B(-4,0) such that AP/AB = 2/5.

$\bf{\Large{\underline{\rm{To\:\:find\::}}}}$

The coordinates of P.

$\bf{\Large{\underline{\tt{\red{Explanation\::}}}}}$

$\bf{Given}\begin{cases}\rm{The\:points\:of\:A\:(-2,3)}\\ \rm{The\:points\:of\:B\:(-4,0)}\end{cases}}$

We know that formula of the coordinates of point P.

$\leadsto\sf{\blue{x\:=\:\frac{mx2+nx1}{m+n} \:\:\:\:,\:\:\:y\:=\:\frac{my2+ny1}{m+n} }}$

We have, $\rm{\frac{AP}{AB} \:=\:\frac{2}{5} }$

$\implies\sf{\frac{AP}{AP+PB} \:=\:\frac{2}{5} }$

$\implies\sf{5AP\:=\:2AP\:+\:2PB}$

$\implies\sf{5AP\:-\:2AP\:=\:2PB}$

$\implies\sf{3AP\:=\:2PB}$

$\implies\sf{\pink{\frac{AP}{BP} \:=\:\frac{2}{3} }}$

Therefore,

P divides AB in the ratio 2:3.

_______________________________________________

$\bf{\Large{\boxed{\sf{Coordinates\:of\:P\::}}}}$

$\longmapsto\sf{x\:=\:\frac{2*(-4)+3*(-2)}{2+3} \:\:\:\:\:\:,\:\:\:\:\:\:y\:=\:\frac{2*0+3*3}{2+3}}$

$\longmapsto\sf{x\:=\:\frac{-8+(-6)}{5} \:\:\:\:\:,\:\:\:\:\:y\:=\:\frac{0+9}{5}}$

$\longmapsto\sf{x\:=\:\frac{-8-6}{5} \:\:\:\:\:,\:\:\:\:y\:=\:\frac{9}{5} }$

$\longmapsto\sf{x\:=\:-\frac{14}{5} \:\:\:\:\:,\:\:\:\:y\:=\:\frac{9}{5} }$

Thus,

$\bf{\Large{\boxed{\rm{The\:coordinates\:of\:P\:is\:\:-\frac{14}{5} \:\:,\:\:\frac{9}{5} }}}}}}$

Answer 2

Answer:

My school's annual function

Step-by-step explanation:

We have to find the coordinates of the point P.

x-coordinate of P = (n1x2 + n2x1 )/n1 + n2

where n1 : n2 is the ratio in which line is to be divided and,

x1 and x2 are the x- coordinates of the points, A and B respectively.

∴ x-coordinate of P = ( 2 × 5 + 3 × 2)/ 2 + 3

= 16/5

Similarly y-coordinate of P = (n1y2 + n2y1 )/n1 + n2

where n1 : n2 is the ratio in which line is to be divided and,

y1 and y2 are the x- coordinates of the points, A and B respectively.

∴ y-coordinate of P = ( 2 × 2 + 3 × -5 )/ 2 + 3

= -11/5

Coordinate of P =(16/5 , -11/5)

∴ It lies in the fourth quadrant.