Question

b) Find the equation of the perpendicular from the point P(-1.-2) on the line 3x + 4y - 12 = 0. Also
find the coordinates of the foot of perpendicular.​

Answer 1

Step-by-step explanation:

Given Find the equation of the perpendicular from the point P(-1.-2) on the line 3x + 4y - 12 = 0. Also  find the coordinates of the foot of perpendicular.

• Equation of straight line in the form of y = mx + c
• The slope of line perpendicular to the line is – 1/m
• Now we have the equation as 3x + 4y = 12 -----------------1
• Now in the form y = mx + c we get
• So y = (-3/4)x + 3
• Slope of a line perpendicular to it will be 4/3
• Equation of all line perpendicular to original line is given by
• So y = (4/3)x + c
• Now perpendicular passes through the point(-1, -2), substituting this we get
• So – 2 = (4/3)(- 1) + c
• Or c = - 2 + 4/3
• Or c = - 2/3
• Substituting C in the above given equation we get
• So y = 4x/3 – 2/3
• Or 4x – 3y = 2 ------------------- 2
• We need to find the point of intersection. So we get
• 3x + 4y = 12 multiply by 4
• 4x – 3y = 2   multiply by 3
• 12x + 16y = 48
• 12x - 9y = 6
• 25 y = 42
• Or y = 42 / 25
• 4x – 3(42/25) = 2
• Or   4x = 2 + 126 / 25
• Or x = 176 / 25 / 4
• Or x = 44/25

Therefore the line and perpendicular intersect at the point (44/25, 42/25

Reference link will be

https://brainly.in/question/1861195