Jitender Gupta and Divya Malik Solutions for Exercise 5: CHALLENGERS

The coordinates of the orthocentre of the triangle, whose vertices are  $\left(-1, 3\right), \left(2, -1\right) \mathrm{and} \left(0, 0\right)$ is 

The point $P\left(-2, 4\right)$ is reflected in the line parallel to $Y-\mathrm{axis}$ at a distance of  $3$ units to the left of  $Y-\mathrm{axis}$ on to the point $P\text{'}$. The point $Q$ is reflected in the origin on to the point $Q\text{'}\left(4, -1\right)$. The equation of the line $P\text{'}Q$is

If the slope of a line passing through the point $A\left(3, 2\right)$ is $\raisebox{1ex}{$3$}\!\left/ \!\raisebox{-1ex}{$4$}\right.$, then the point on the line, which are $5$ units away from the point $A$ is 

A ray of light coming from the point $\left(1, 2\right)$ is reflected at a point $A$ on the $X-\mathrm{axis}$ and then passes through the point $\left(5, 3\right)$, then coordinates of the point $A$ is 

A line passes through the point $\left(3, -2\right)$. The locus of the middle point of the portion of the line intercepted between axes is

If the image of point $\left(2, 1\right)$ with respect to the line mirror be $(5, 2)$, then the equation of the mirror is,

Suppose the equation of the line through the point $\left(0,2\right)$ making an angle $\frac{2\mathrm{\pi }}{3}$ with the positive  $X$-axis. Find the equation of the line parallel to the given line and below the origin, which is equidistant from origin .                   ( Given, $\tan \left(\mathrm{\pi }-\mathrm{\theta }\right)=-\tan \theta$).

Suppose $ABC$ be a triangle, whose centroid is $G$. If the coordinates of $B,C$ and $G$ are $\left(-2,0\right),\left(3,1\right)$ and $\left(1,5\right)$, then the equations of the sides $AB$ and $AC$ are respectively