# Answer the following question: Find the co-ordinates of the foot of the perpendicular drawn from the point P(−1, 3) the line 3x − 4y − 16 = 0 - Mathematics and Statistics

Diagram
Sum

Find the co-ordinates of the foot of the perpendicular drawn from the point P(−1, 3) the line 3x − 4y − 16 = 0

#### Solution

Let M be the foot of perpendicular drawn from P(–1, 3) to the line

3x – 4y – 16 = 0   ...(i)

Slope of the line 3x – 4y – 16 = 0 is

(-3)/(-4) = 3/4

Since PM ⊥ to line (i),

slope of PM = (-4)/3

∴ Equation of PM is

y – 3 = (-4)/3(x + 1)

∴ 3(y – 3) = –4(x + 1)

∴ 3y – 9 = – 4x – 4

∴ 4x +  3y – 5 = 0  ...(ii)

The foot of perpendicular i.e., point M, is the point of intersection of equation (i) and (ii).

By (i) x 3 + (ii) x 4, we get

25x = 68

∴ x = 68/25

Substituting x = 68/25 in (ii), we get

4(68/25) + 3y - 5 = 0

∴ 3y = 5 - 4(68/25) = (125 - 272)/25 = (-147)/25

∴ y = (-49)/25

∴ The co-ordinates of the foot of perpendicular M are (68/25, (-49)/25).

Is there an error in this question or solution?

#### APPEARS IN

Balbharati Mathematics and Statistics 1 (Arts and Science) 11th Standard Maharashtra State Board
Chapter 5 Straight Line
Miscellaneous Exercise 5 | Q II. (26) | Page 126