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

The area of a triangle is $5$ and two of its vertices are $A(2,1), B(3,-2).$ Then, the third vertex, in $1^{st}$ quadrant which lies on the line $y=x+3$ is

The line $x+y=4$ divides the line joining the points $\left(-1, 1\right)$ and $\left(5, 7\right)$ in the ratio

The line $3x+4y-24=0$ intersects the $X-$axis at $A$ and $Y-$axis at $B.$ Then, the circumcentre of the $△OAB,$ where $O$ is the origin, is 

A straight line passes through the points $\left(5,0\right)$ and $\left(0,3\right)$. The length of the perpendicular from the point $\left(4,4\right)$ on the line is

The distance of the point $\left(1,3\right)$ from the line $2x+3y=6$, measured parallel to the line $4x+y=4$, is

What is the equation of the line which passes through $\left(4,-5\right)$ and is perpendicular to $3x+4y+5=0$?

If a line is perpendicular to the line $5x-y=0$ and forms a triangle of area $5$ square units with coordinate axes, then its equation is

The lines $(a+2\mathrm{b}) x+(a-3\mathrm{b}) y=a-b$ for different values of $a$ and $b$ pass through the fixed point whose coordinates are