For the straight line 8x-15y+51=0, Find the length of the perpendicular from the origin to this line and the inclination - Maths - Straight Lines

Question

For the straight line 8x-15y+51=0, Find the length of the
perpendicular from the origin to this line and the inclination of
this perpendicular with the x axis

Mayank Jha · Accepted Answer

Dear student,

The given straight line is:8x - 15y + 51 = 0 We know that, The distance from a point (m, n) to the line Ax + By + C = 0 is given by:d= |Am + Bn + C|A² + B²∴Length of the perpendicular from the origin will be = |0 + 0 + 51|8² + 15² = 5117 = 3Also, 8x - 15y + 51 = 0 ⇒-15y = -8x - 51⇒y = 815x + 5115 Slope of this line will be(m1): 815Slope of the line perpendicular to this line will be(m2) = -158∴Inclination of this perpendicular with thw x-axis = tan-1(-158) = -61
93°

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For the straight line 8x-15y+51=0, Find the length of the perpendicular from the origin to this line and the inclination of this perpendicular with the x axis