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 Apr, 2014, 09:00: AM

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  | 30th Apr, 2014, 11:00: AM