Question

The foot of the perpendicular from (-3, 7) to the line 3x – 4y + 12 = 0 is
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Answer 1

Answer:

The foot of the perpendicular is the point (0,3)

Step-by-step explanation:

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Answer 2

SOLUTION ::

The given equation of the line is

3x - 4y + 12 = 0 - - - - - - - (1)

Let the line perpendicular to Equation (1) is

4x + 3y + k = 0 - - - - - - - - (2)

where c = constant

Now Equation (2)passes through ( -3 , 7)

So

4 (-3) + 3 ×7 + k= 0

- 12+ 21 + c = 0

9 + k = 0

k = - 9

So Equation (2) converted into

4x + 3y - 9 = 0 - - - - - - - (3)

Now we find the point of intersection to get the required point

Multiplying Equation (1) by 3 & Equation (3) by 4 we get

9x - 12y + 36 = 0

16x + 12y - 36= 0

Addition gives

25x = 0

x = 0

From Equation (1)

-4y + 12 = 0

4y = 12

y = 3

So the required foot of the perpendicular from (-3, 7) to the line 3x – 4y + 12 = 0 is ( 0, 3)

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