Straight Lines

What is the ratio in which the point $C\left(-\frac{2}{7},-\frac{20}{7}\right)$ divides the line joining the points $\mathrm{A}(-2,-2)$ and $\mathrm{B}(2,-4)$ ?

Consider the triangle $A B C$ with vertices $A(-2,3), B(2,1)$ and $C$ $(1,2)$. What is the centroid of the tirnalge ABC ?

The two vertices of an equilateral triangle are $(0,0)$ and $(2,2)$. Consider the following statements : The third vertex has at least one irrational coordinate. The area is irrational. Which of the above statements…

What is the equation of the straight line cutting off an intercept 2 from the negative direction of $y$-axis and inclined at $30^{\circ}$ with the positive direction of $x$-axis?

$(a, 2 b)$ is the mid-point of the line segment joining the points $(10,-6)$ and $(k, 4)$. If $a-2 b=7$, then what is the value of $k$ ?

ABC is an acute angled isosceles triangle. Two equal sides AB and AC lie on the lines $7 x-y-3=$ 0 and $x+y-5=0$. If $\theta$ is one of the equal angles, then what is $\cot \theta$ equal to?

The coordinates of three consecutive vertices of a parallelogram $A B C D$ are $A(1,3), B(-1,2)$ and $C(3,5)$. What is the equation of the diagonal BD?

The number of points represented by the equation $x=5$ on the $x y$-plane is:

Consider a parallelogram whose vertices are $\mathrm{A}(1,2), \mathrm{B}(4$, y), $\mathrm{C}(\mathrm{x}, 6)$ and $\mathrm{D}(3,5)$ taken in order. What is the value of $\mathrm{AC}^2-\mathrm{BD}^2$ ?

Two straight lines passing through the point $\mathrm{A}(3,2)$ cut the line $2 \mathrm{y}=\mathrm{x}+3$ and x -axis perpendicularly at P and Q respectively. The equation of the line PQ is

The length of perpendicular from the origin to a line is 5 units and the line makes an angle $120^{\circ}$ with the positive direction of $x$-axis. The equation of the line is

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