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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 30th April 2014, 9:00 AM
Answered by Expert
Answer:

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

x equals 367 over 241 space a n d space y equals 371 over 241
Therefore, the foot of the perpendicular is given by

open parentheses 367 over 241 comma space 371 over 241 close parentheses
Answered by Expert 30th April 2014, 11:00 AM
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