CBSE Class 11-science Answered
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
![Double click to edit](https://images.topperlearning.com/topper/questions/11283_8a1fdba5bd39fa1a24fd94a6dca0408a.png)
![Double click to edit](https://images.topperlearning.com/topper/questions/11283_8a1fdba5bd39fa1a24fd94a6dca0408a.png)
Therefore the equation of a line passing through the point (3, -4) and perpendicular to the given line is
15x + 4y - 29 = 0 ... (ii)
![Double click to edit](https://images.topperlearning.com/topper/questions/11283_8a1fdba5bd39fa1a24fd94a6dca0408a.png)
Solving equation (i) and (ii), we get
![x equals 367 over 241 space a n d space y equals 371 over 241](https://images.topperlearning.com/topper/tinymce/cache/209fcf737bb93727500d7cded4f78982.png)
Therefore, the foot of the perpendicular is given by
![open parentheses 367 over 241 comma space 371 over 241 close parentheses](https://images.topperlearning.com/topper/tinymce/cache/b36cd142b6a957265b005da6520e1bde.png)
Answered by | 30 Apr, 2014, 11:00: AM
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