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Find the coordinates of the foot of the perpendicular from the point (3, -4) to the line 4x - 15y + 17 = 0.
Asked by Topperlearning User | 30 Apr, 2014, 09:00: AM

The equation of the given line is 4x - 15y + 17 =   0            ...  (i)

The equation of a line perpendicular to the given line is 15x + 4y - k = 0, where k is a constant.
If this line passes through the point (3, -4), then
15 x 3 + 4 x (-4) - k = 0
45 - 16 - k = 0
k = 29
Therefore the equation of a line passing through the point (3, -4) and perpendicular to the given line is
15x + 4y - 29 = 0                                         ...    (ii)

The required foot of the perpendicular is the point of intersection of lines (i) and (ii).
Solving equation (i) and (ii), we get

Therefore, the foot of the perpendicular is given by

Answered by | 30 Apr, 2014, 11:00: AM

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