Odisha Board Solutions for Chapter: Straight Lines, Exercise 1: EXERCISES 11 (a)

The distance between the following pairs of points (in units) $\left(3, 4\right)\left(-2, 1\right)$ is $\sqrt{k}$, then the value of $k$ is

The distance between the following pairs of points (in units) $\left(-1, 0\right), \left(5, 3\right)$ is $k\sqrt{5}$.

The value of $k$ is $?$

Find the area of the triangle(in sq units) whose vertices are $\left(1, 2\right), \left(3, 4\right), \left(\frac{1}{2}, \frac{1}{4}\right).$

If the area of the triangle with vertices $\left(0, 0\right), \left(1, 0\right), \left(0, a\right)$ is $10$ units, find the value of $a.$

Find the value of $a$ so that the points $\left(1, 4\right), \left(2, 7\right), \left(3, a\right)$ are collinear.

Find the slope of the lines whose inclinations are given.

$45°,$

Find the slope of the line whose inclination is given.

$135°$

Prove analytically:

An angle in a semicircle is a right angle.