Question

the inclination of the line passing through the points(-2,3)and (-1,4) is
a)π/4
b)π/3
c)π/6
d)3π/4
​noo need I got the answer is option a

Answer 1

a) $\frac{\pi }{4}$

• We have seen lines drawn on the coordinate plane in geometry. The best approach to determine without using any geometrical tools if the lines are parallel, perpendicular, or at any angle is to measure the slope. A line's slope in mathematics is defined as the ratio of the change in the y coordinate to the change in the x coordinate. Both the net change in the y-coordinate and the net change in the x-coordinate are denoted by y and x, respectively.
• A line's slope often indicates the steepness and direction of the line. By calculating the difference between the coordinates of the two points, (x1,y1) and (x2,y2), it is simple to calculate the slope of a straight line between them. The letter "m" is frequently used to denote slope.

Here, according to the given information, we are given that,

The points are (-2,3)and (-1,4).

Now, we know that,

$m=\frac{y_{2}-y_{1} }{x_{2}-x_{1} } =\frac{4-3}{-1+2} =\frac{1}{1} =1$

Now, $tan\alpha =1$

Or, $\alpha =\frac{\pi }{4}$.

Hence, option a is correct.

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