Question

$\huge \mathcal \green{Question}$​

Answer 1

Explanation:

Equation of the perpendicular from the point.

p(1, -2) on the line 4x - 3y - 5 = 0.

As we know that,

Slopes of the perpendicular line = m = b/a.

Slopes of the line : 4x - 3y - 5 = 0.

☞m = -3/4

As we know that,

Formula of the Equation of the line.

☞ (y - y1) = m(x - x1).

Using this formula in the equation, we get.

☞ ( y - (-2)) = (-3/4)(x - 1).

☞ (y + 2) = (-3/4)(x - 1).

☞ 4(y + 2) = - 3(x - 1).

☞ 4y + 8 = 3x + 3.

☞ 4y + 3x + 8 - 3 = 0.

☞ 3x + 4y + 5 = 0

To find :

Co-ordinates of the foot of the perpendicular.

☞ 4x - 3y - 5 = 0. - - - - - (1).

☞ 3x + 4y + 5 = 0. - - - - - (2).

From equation (1) and (2), we get.

Multiply equation (1) by 4.

Multiply equation (2) by 3.

☞4x - 3y - 5 = 0. - - - - - (1). × 4.

☞3x + 4y + 5 = 0. - - - - - (2). × 3.

☞16x - 12y - 20 = 0. - - - - - (3).

☞9x + 12y + 15 = 0. - - - - - (4).

According equation (3) and (4), we get.

☞25x - 5 = 0.

☞25x = 5.

☞5x = 1.

☞x = 1/5.

Put the value of x = 1/5 in equation (2), we get.

☞3x + 4y + 5 = 0.

☞3(1/5) + 4y + 5 = 0.

☞(3/5) + 4y + 5 = 0.

☞(3 + 20y + 25)/5 = 0

☞3 + 20y + 25 = 0.

☞20y + 28 = 0.

☞20y = - 28.

☞5y = - 7.

☞y = - 7/5.

• Their co-ordinates = (1/5, - 7/5)

Answer 2

THRIR CO-ORDINATES=(1/5,-7/5)