Answer:
The inclination of the through the points (5, 14) and (9, 18) is 45°
Step-by-step 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
[tex]m = \dfrac{y_2 - y_1}{x_2-x_1}[/tex]
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;
[tex]m = \dfrac{18 - 14}{9-5} = \dfrac{4}{4} = 1[/tex]
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;
[tex]tan^{-1}m = tan^{-1} \left (\dfrac{y_2 - y_1}{x_2-x_1} \right) = \theta[/tex]
given that m = 1, we have;
tan⁻¹(m) = θ = tan⁻¹(1) = 45°.
