Q. 21

# Find the coordinates of the foot of the perpendicular from the point (-1, 3) to the line 3x – 4y – 16 = 0.

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.

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

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