Embibe Experts Solutions for Chapter: Straight Line, Exercise 1: Exercise 1

If $\left(3,-4\right)$ and $\left(-6,5\right)$ are the extremities of a diagonal of a parallelogram and $\left(2,1\right)$ is the third vertex, then its fourth vertex is-

The point $A$ divides the join of the points $\left(-5,1\right)$ and $\left(3,5\right)$ in the ratio $k:1$ and coordinates of points $B$ and $C$ are $\left(1,5\right)$ and $\left(7,-2\right)$ respectively. If the area of $\Delta ABC$ be $2$ units, then $k$ equals-

If an equilateral triangle, having centroid at the origin, has a side along the line, $x+y=2,$ then the area (in sq units) of this triangle is

Consider a $∆ABC$ with vertices at $(0,-3)(-2\sqrt{3},3)$ and $(2\sqrt{3},3)$, respectively. The incentre of the triangle with vertices at the mid-points of the sides of $\Delta ABC$ is

A line passing through the point $P\left(1,2\right)$ meets the line $x+y=7$ at a distance of $3$ units from $P$. Then, the slope of this line satisfies the equation

The equation of a straight line, which passes through the point $\left(-3,5\right)$ such that the portion of it between the axes is divided by the point in the ratio $5:3$ internally (reckoning from $x$-axis), will be-

The equation of perpendicular bisector of the sides $AB$ and $AC$ of a $∆ABC$ are $x-y+5=0$ and $x+2y=0,$ respectively. If the point $A$ is $\left(1,-2\right),$ then the equation of line $BC$ 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