Question

hloo....
plzz answer this question..
find the coordinates of point R on the line segment joining the pts. (-1,3) and Q(2,5) such that PR=3/5PQ​

Answer 1

Answer :

The coordinates of R is ( 4/5 , 21/5)

Given :

• The points are P(-1 , 3) and Q(2 , 5)
• The point R on the line PQ divides PQ such that PR= 3/5PQ

To Find :

• The coordinates of R

Formula to be used :

Section formula : (x₁ , y₁) and (x₂ , y₂) are two points and a point (x , y) divides the line joining these points in the ration m : n then

$\sf{x = \dfrac{ mx_{2} + nx_{1}}{m + n} }$

$\sf{y = \dfrac{my_{2} + ny_{1} }{m + n} }$

Solution :

From a given condition :

$\sf{PR = \dfrac{3}{5} \times PQ } \\ \implies \sf{5PR} = 3PQ$

Now we have :

$\implies \sf{3PQ = 3PR + 3QR} \\ \implies\sf 5PR = 3PR + 3QR\\\implies \sf 3QR = 2PR\\\implies \sf{QR =\frac{2}{3}PR }$

So ratio is :

$\sf \dfrac{PR }{QR} = \dfrac{PR}{ \dfrac{2}{3} PR} \\ \implies\sf \dfrac{PR }{QR} = \dfrac{3}{2}$

Now using the section formula to find coordinates of R .

Consider R( x , y)

$\sf{x = \dfrac{(2 )\times 3 + ( - 1) \times 2}{3 + 2} } \\ \\ \implies \sf{x = \dfrac{6 - 2}{5} } \\ \\ \implies \sf{x = \dfrac{ 4}{5} }$

and now for Y - co-ordinate

$\sf \implies y = \dfrac{( 5) \times 3 + (3) \times 2}{3 + 2} \\ \\ \implies \sf{y = \dfrac{15 +6 }{5} } \\ \\ \implies \sf{y = \dfrac{21}{5} }$