Question

if (2,-3) is the foot of the perpendicular from (-4,5)on a line ,then the equation of the line is​

Answer 1

The equation of the straight line passing through the points (2, - 3) and (- 4, 5) is

y - (- 3) = {5 - (- 3)}/(- 4 - 2) * (x - 2)

or, y + 3 = - 8/6 * (x - 2)

or, y + 3 = - 4/3 * (x - 2)

or, 3y + 9 = - 4x + 8

or, 4x + 3y + 1 = 0 .....(1)

Then the line perpendicular to the straight line (1) is given by

3x - 4y = c .....(2)

This line passes through the point (2, - 3).

Then,

3 (2) - 4 (- 3) = c

or, 6 + 13 = c

or, c = 18

Therefore the required straight line is

3x - 4y = 18.

Read more on Brainly:

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2. Find the equation of the line passing through the point (4,5) & perpendicular to the line 7x-5y=420 - https://brainly.in/question/12908911

Answer 2

The equation of the line is 3x - 4y = 18

Step-by-step explanation:

Let the points (2, -3) and (-4, 5) be the line AB. The base of AB be CD.

The slope of the line AB is:

m₁ = (y₂ - y₁)/(x₂ - x₁)

On substituting the values, we get,

m₁ = (5 - (-3))/(-4 - 2) = (5 + 3)/(-6)

∴ m₁ = -8/6 = -4/3

The slope of the line CD is:

m₂ = 1/m₁

m₂ = 1/(4/3)

∴ m₂ = 3/4

The formula of the line question is:

y - y₁ = m(x - x₁)

On substituting the formula, we get,

y - (-3) = 3/4 (x - 2)

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

4y + 12 = 3x - 6

3x - 4y - 18 = 0

∴ 3x - 4y = 18