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  • Point R (h, k) divides a line segment between the axes in the ratio 1: 2. Find equation of the line.

Q : 19     Point  R(h,k)  divides a line segment between the axes in the ratio 1:2 .  Find  equation of the line.

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Let the coordinates of Point A is (x,0) and of point B is (0,y)
It is given that point R(h , k) divides the line segment between the axes in the ratio 1:2
Therefore,
R(h , k) =\left ( \frac{1\times 0+2\times x}{1+2},\frac{1\times y+2\times 0}{1+2} \right )=\left ( \frac{2x}{3},\frac{y}{3} \right )
h = \frac{2x}{3} \ \ and \ \ k = \frac{y}{3}
x = \frac{3h}{2} \ \ and \ \ y = 3k
Therefore, coordinates of point A is \left ( \frac{3h}{2},0 \right )  and of point B is (0,3k)
Now, slope of line passing through points \left ( \frac{3h}{2},0 \right ) and (0,3k)  is 
m = \frac{3k-0}{0-\frac{3h}{2}}= \frac{2k}{-h}
Now, equation of line passing through point (0,3k)  and with slope -\frac{2k}{h} is 
(y-3k)=-\frac{2k}{h}(x-0)
h(y-3k)=-2k(x)
yh-3kh=-2kx
2kx+yh=3kh
Therefore, the equation of line is 2kx+yh=3kh

Posted by

Gautam harsolia

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