Question

Find the inclination of the line passing through points

A (-1 ,-√2) and B (√3 ,3)​

Answer 1

Answer:

value of inclination is 58°

Step-by-step explanation:

the explanation is given above

Answer 2

Given:

Two points A (-1, -√2) and B (√3, 3)​.

To Find:

The inclination of the line that is passing through the points A (-1, -√2) and B (√3, 3)​.

Solution:

The inclination of any line is also called the slope of the line. The slope of the line is given by,

${\rm slope}=\frac{y_2-y_1}{x_2-x_1}$

The slope of the line is equal to $tan\theta$ or 'm'.

Substitute $-1$ for $x_1$, $-\sqrt{2}$ for $y_1$, $\sqrt{3}$ for $x_2$, and 3 for $y_2$ into the slope formula and simplify.

${\rm slope}=\frac{3-(-\sqrt{2}) }{\sqrt{3}-(-1) } \\=\frac{3+\sqrt{2} }{\sqrt{3}+1 }\\=\frac{3+1.414}{1.732+1}\\ =\frac{4.414}{2.732}\\ =1.616$

Equate 1.616 to $tan\theta$ and find $\theta$.

$tan\theta=1.616\\\theta=tan^{-1}(1.616)\\=1.02\, {\rm radian}$

Convert 1.02 radian into degrees by multiplying it by $\frac{180}{\pi}$.

$\theta=1.02\times \frac{180}{\pi}\\ =58.02^{\circ}$

Thus, the inclination of the line passing through the points A (-1, -√2) and B (√3, 3)​ is 58 degrees.