Given: equation is perpendicular from the point (-1, 3) to the line 3x – 4y – 16 = 0.
To find:
The coordinates of the foot of the perpendicular from the point (-1, 3) to the line 3x – 4y – 16 = 0.
Explanation:
Let A (− 1, 3) be the given point. Also, let M (h, k) be the foot of the perpendicular drawn from A (− 1, 3) to the line 3x − 4y − 16 = 0
Diagram:
Point M (h, k) lies on the line 3x − 4y − 16 = 0
3h − 4k − 16 = 0 … (1)
Lines 3x − 4y − 16 = 0 and AM are perpendicular.
∴ \(\frac{k-3}{h+1}\times\frac{3}{4}\) = -1
⇒ 4h + 3k – 5 = 0 … (2)
Solving eq (1) and eq (2) by cross multiplication, we get:
Hence, the coordinates of the foot of perpendicular are \(\Big(\frac{68}{25},-\frac{49}{25}\Big)\)
