Embibe Experts Solutions for Chapter: Point and Straight Line, Exercise 1: Exercise-1

Find the points which trisects the line segment joining $\left(0,0\right)$ and $\left(9,12\right)$.

Find the harmonic conjugate of the point $R\left(5,1\right)$ with respect to points $P\left(2,10\right)$ and $Q\left(6,-2\right)$.

Find the area of the quadrilateral with vertices as the points given in following: $\left(0,0\right), \left(a,0\right), \left(a,b\right), \left(0,b\right)$

$\left(\mathrm{ii}\right)$ $2x+5y\le 10$

$\left(\mathrm{iii}\right)$ $8x+3y+6>0$

Plot the region, $x>2$

$\left(\mathrm{ii}\right)$ The intersection of the lines $x+2y+3=0$ and $3x+4y+7=0$ and perpendicular to the straight line $y-x=8$.

If the pair of lines represented by equation $k\left(k-3\right)x^2+16xy+\left(k+1\right)y^2=0$ are perpendicular to each other, then find $k$.