Question

A straight line is parallel to the line $y=2x$ passes through $Q(2,3)$ and cuts the line$2x+4y-21=0$ at $P$ then find the coordinates of P

Answer 1

$\begin{array}{c}\text{Equation of line}11\text{to the line}y-2x=0\text{will}\\ \text{be}y-2x\ne k\text{. It passes through}(2,3)\\ \therefore 3-2\left(2\right)=k\Rightarrow k=-1\\ \text{Hence,}e{q}^n\text{of}\mathrm{lin}e=y-2x+1=0\\ \text{it cuts the line}2x+4y-21=0\text{at}P\text{point}\\ \therefore \text{solving both the equations we get}\\ y=4\text{and}x=2.5\\ P(2.5,4)\end{array}$