Question

What is the inclination of a line through the points(5,14) and (9,18)

Answer 1

The inclination of the through the points (5, 14) and (9, 18) is 45°

Explanation:

The given point has coordinates (5, 14) and (9, 18)

To find the inclination, θ, of the line passing the two points, with point 1 having coordinates (x₁, y₁) and point 2, having coordinates (x₂, y₂), we have to look for the slope as follows;

The slope, m = Change in the y-coordinate ÷ Change in the x-coordinate

`m = (y_2 - y_1)/(x_2-x_1)`

Where:

y₁ = The y-coordinate of point 1 = 14

x₁ = The x-coordinate of point 1 = 5

y₂ = The y-coordinate of point 2 = 18

x₂ = The x-coordinate of point 2 = 9

Substituting, we have;

`m = (18 - 14)/(9-5) = (4)/(4) = 1`

The inclination of the line is the angle the line makes with x-axis

Since the slope gives the ratio of the opposite and adjacent segment to the angle of inclination, the arc-tangent of the slope will give the angle in degrees as follows;

`tan^(-1)m = tan^(-1) \left ((y_2 - y_1)/(x_2-x_1) \right) = \theta`

given that m = 1, we have;

tan⁻¹(m) = θ = tan⁻¹(1) = 45°.