R D Sharma Solutions for Chapter: The Straight Lines, Exercise 1: EXERCISE 23.1

Find the slope of the line which make the following angle with the positive direction of positive $x-$axis.

$-\frac{\pi }{4}$

Find the slope of a line passing through the following points:

$\left(a{t}_1^2,2a{t}_1\right)$ and $\left(a{t}_2^2,2a{t}_2\right)$

Without using the distance formula, show that points $(-2,-1), (4,0), (3,3), \text{and} (-3,2)$ are the vertices of a parallelogram.

Find the angle (in degrees) between the $X$ -axis and the line joining the points $(3,-1)$ and $(4,-2)$

Line through the points $(-2,6)$ and$(4,8)$ is perpendicular to the line through the points $(8,12)$ and $(x, 24)$. Find the value of $x$

Find the value of $x$ for which the points $(x,-1), (2,1)$ and $(4,5)$are collinear.

If the angle between $X$ -axis and the line joining the points $(3,-1)$ and $(4,-2)$ is $\frac{k\mathrm{\pi }}{4}$, then find the value of $k$.

By using the concept of slope, show that the points $(-2,-1), (4,0), (3,3)$ and $(-3,2)$ are the vertices of a parallelogram.