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  • A line intersects the y-axis and x-axis at the points P and Q respectively. If (2, - 5) is the mid-point of PQ, then find the coordinates of P and Q.      

A line intersects the y-axis and x-axis at the points P and Q respectively. If (2, - 5) is the mid-point of PQ, then find the coordinates of P and Q.

 

 

 

 
 
 
 
 

Answers (1)

Let mid point of PQ be R

\Rightarrow R=(2,-5)

Coordinates of  P=(0,y)=(x_1,y_1)

Coordinates of  Q=(x,0)=(x_2,y_2)

Using section formula :

R=(2,-5)=\left ( \frac{mx_2+nx_1}{m+n},\frac{my_2+ny_1}{m+n} \right )

We know that 

\frac{PR}{QR}=\frac{m}{n}=\frac{1}{1}

\Rightarrow (2,-5)=\left ( \frac{1\times x+1\times 0}{1+1},\frac{1\times 0+1\times y}{1+1} \right )

\Rightarrow (2,-5)=\left ( \frac{x}{2},\frac{y}{2} \right )

\Rightarrow \frac{x}{2}=2;\: \frac{y}{2}=-5

\Rightarrow x=4;\: y=-10

Coordinates of  P=(0,-10)

Coordinates of  Q=(4,0)

Posted by

Ravindra Pindel

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