Question

$\huge \mathfrak \green{Question}$​

Answer 1

Step-by-step explanation:

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Answer 2

Answer:

☈

➲ Solution

➥ Given Line :-

➻ 4x - 3y - 5 = 0

➻ Slope of Given Line

➻ 4x - 3y - 5 = 0 is

➾ - 3y = -4x + 5

➾ y = -4/3 x +5

➻ Therefore, The slope of given line is 4/3

➻ Slope of perpendiular line

➾ -3/4

➲ To Find :-

➻ The equation of the perpendicular from the point P(1, -2) on the line 4x - 3y - 5 = 0.

➻ Co-ordinates of the foot of the perpendicular

➲ Explanation :-

⌦ Equation of given line

➠ y -y 1= m( x -x 1)

➠ y + 2 = -3/4 (x-1)

➠ 4 × (y + 2 ) = -3 × (x-1)

➠ 4 y + 8 = -3 x +3

➠ 3x +4y = 3-8

➪ 3x +4y = -5

➲ Now

⌦ 4x - 3y -5 = 0 equation (1)

⌦ 3 x +4y +5 = 0 equation (2)

➲Solving equation

(1) and (2) ,we get

⌦ 4x - 3y -5 = 0

can be written as

➠ 4x-3y = 5 - - equation (1)

⌦ 3 x +4y +5 = 0

can be written as

➠ 3 x +4y = -5 - - equation (2)

➲ Now

➠ 4x-3y = 5 - equation (1)

multiply by 3

➠ 12 x -9 y = 15

➠3 x +4y = -5 = - equation (2)

multiply by 4

➠ 12 x + 16 y = - 20

➲ Solving equation

➠ 12 x -9 y = 15 and

12 x + 16 y = - 20

⇾⇾⇾⇾12 x - 9 y = 15

⇾⇾⇾⇾12 x + 16 y = - 20

______(-)___(-)____(+)_________

➾➾➾➾ -25 y = 35

➠ y = -35/25

➠ y = -35÷5/25÷5

➠ y = -7 / 5

➲ Place y = -7 /5 in equation (1) that is 4x-3y = 5

➠ 4x-3 ×( -7 /5) = 5

➠ 4x + 21/5 =5

➠ 4x = 5 - 21/5

➠ 4x = 4/ 5

➠ x = 1 / 5

➲ Therefore

⌦ The coordinates of foot of perpendicular are

$\sf \huge \boxed{\implies{( \frac{1}{5} , \frac{ - 7}{5}) }}$