Equally inclined lines mean: the lines which make equal angles with both the coordinate axes.
PICCCCCCCCCCC
The above diagram shows two equally inclined lines AB and CD.
As is clear from the above diagram:
For AB: Inclination θ = 45°,
Therefore, slope = tan 45° = 1.
For CD: Inclination θ = 45°,
Therefore, slope = tan (45°) = 1.
Solved example on equally inclined lines:
Find the equation of the lines which is passes through the point (2. 3) and equally inclined to the coordinate axes.
Solution:
As is clear from the diagram, there are two lines AB and CD, equally inclined to the coordinate axes.
For line AB: m = tan 45° = 1
and (x\(_{1}\), y\(_{1}\)) = (2, 3)
Therefore, its equation: y – y\(_{1}\) = m(x – x\(_{1}\))
⟹ y – 3 = 1(x + 2)
⟹ y  3 = x + 2
⟹ y = x + 5
For line CD: m = tan (45°) = 1
and (x\(_{1}\), y\(_{1}\)) = (2, 3)
Therefore, its equation: y – y\(_{1}\) = m(x – x\(_{1}\))
⟹ y – 3 = 1(x + 2)
⟹ y  3 = x  2
⟹ y = x + 1
Therefore, the required equations are y = x + 5 and y = x + 1
From Equally Inclined Lines to HOME
Didn't find what you were looking for? Or want to know more information about Math Only Math. Use this Google Search to find what you need.

New! Comments
Have your say about what you just read! Leave me a comment in the box below. Ask a Question or Answer a Question.