Equally Inclined Lines

Equally inclined lines mean: the lines which make equal angles with both the co-ordinate axes.

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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 co-ordinate axes.

Solution:

As is clear from the diagram, there are two lines AB and CD, equally inclined to the co-ordinate 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





10th Grade Math

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