Arun Sharma Solutions for Exercise 2: Level of Difficulty

The orthocenter of the triangle formed by the points. $(0, 0), (8, 0)$ and $(4, 6)$ is:

The area of a triangle is $5$ square units, two of its vertices are $(2, 1)$ and $(3,-2)$. The third vertex lies on $y = x + 3$. What will be the third vertex?

The equations of two equal sides $AB$ and $AC$ of an isosceles triangle $ABC$ are $x + y = 5$ and $7x - y = 3$ respectively. What will be the equation of the side $BC$ if area of triangle $ABC$ is $5$ square units.

Three vertices of a rhombus, taken in order are $(2, -1), (3, 4)$ and $(-2, 3)$. Find the fourth vertex.

Four vertices of a parallelogram taken in order are $(-3, -1), (a, b), (3, 3)$ and $(4, 3)$. What will be the ratio of $a$ to $b$?

What will be the new equation of a straight line $3x + 4y = 6$ if the origin gets shifted to $(3, – 4)$? 

What will be the value of $p$ if the equation of straight line $2x + 5y = 4$ gets changed to $2x + 5y = p$ after shifting the origin at $(3, 3)$?

A line passing through the points $(\alpha ,2\alpha )$ and $(-2,3)$ is perpendicular to the line $4x+3y-7=0$, find the value of $\alpha$.