The line 4x - 3y + 12 = 0 meets the x-axis at A. Write the co-ordinates of A. Determine the equation of line through A and perpendicular to 4x - 3y + 12 = 0.

At A, y co-ordinate = 0 as it lies on x-axis. A = (x, 0) Substituting y = 0 in equation 4x - 3y + 12 = 0 we get, ⇒ 4x - 3(0) + 12 = 0 ⇒ 4x + 12 = 0 ⇒ 4x = -12 ⇒ x = -3. A = (x, 0) = (-3, 0). Given, ⇒ 4x - 3y + 12 = 0 ⇒ 3y = 4x + 12 ⇒ y = + 4 Comparing above equation with y = mx + c we get, m = . Let slope of line perpendicular to 4x - 3y + 12 = 0 be m 1 . ∴ Product of their slopes will be equal to -1. ∴ m × m 1 = -1 ⇒ ⇒ . By point slope form, Equation of line through A and slope = , ⇒ y - y 1 = m(x - x 1 ) ⇒ y - 0 = [x - (-3)] ⇒ 4y = -3(x + 3) ⇒ 4y = -3x - 9 ⇒ 3x + 4y + 9 = 0. Hence, equation of line through A and perpendicular to 4x - 3y + 12 = 0 is 3x + 4y + 9 = 0.

A(1, -5), B(2, 2) and C(-2, 4) are the vertices of triangle ABC. Find the equation of :
(i) the median of the triangle through A.
(ii) the altitude of the triangle through B.
(iii) the line through C and parallel to AB.

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(i) Write down the equation of the line AB, through (3, 2) and perpendicular to the line 2y = 3x + 5.
(ii) AB meets the x-axis at A and the y-axis at B. Write down the co-ordinates of A and B. Calculate the area of triangle OAB, where O is the origin.

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The point P is the foot of perpendicular from A(-5, 7) to the line 2x - 3y + 18 = 0. Determine :
(i) the equation of the line AP
(ii) the co-ordinates of P

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Th points A, B and C are (4, 0), (2, 2) and (0, 6) respectively. Find the equations of AB and BC.
If AB cuts the y-axis at P and BC cuts the x-axis at Q, find the coordinates of P and Q.

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Mathematics

The line 4x - 3y + 12 = 0 meets the x-axis at A. Write the co-ordinates of A.
Determine the equation of line through A and perpendicular to 4x - 3y + 12 = 0.

Straight Line Eq

Related Questions

A(1, -5), B(2, 2) and C(-2, 4) are the vertices of triangle ABC. Find the equation of :
(i) the median of the triangle through A.
(ii) the altitude of the triangle through B.
(iii) the line through C and parallel to AB.

(i) Write down the equation of the line AB, through (3, 2) and perpendicular to the line 2y = 3x + 5.
(ii) AB meets the x-axis at A and the y-axis at B. Write down the co-ordinates of A and B. Calculate the area of triangle OAB, where O is the origin.

The point P is the foot of perpendicular from A(-5, 7) to the line 2x - 3y + 18 = 0. Determine :
(i) the equation of the line AP
(ii) the co-ordinates of P

Th points A, B and C are (4, 0), (2, 2) and (0, 6) respectively. Find the equations of AB and BC.
If AB cuts the y-axis at P and BC cuts the x-axis at Q, find the coordinates of P and Q.

Mathematics

The line 4x - 3y + 12 = 0 meets the x-axis at A. Write the co-ordinates of A.Determine the equation of line through A and perpendicular to 4x - 3y + 12 = 0.

Straight Line Eq

Related Questions

A(1, -5), B(2, 2) and C(-2, 4) are the vertices of triangle ABC. Find the equation of :(i) the median of the triangle through A.(ii) the altitude of the triangle through B.(iii) the line through C and parallel to AB.

(i) Write down the equation of the line AB, through (3, 2) and perpendicular to the line 2y = 3x + 5.(ii) AB meets the x-axis at A and the y-axis at B. Write down the co-ordinates of A and B. Calculate the area of triangle OAB, where O is the origin.

The point P is the foot of perpendicular from A(-5, 7) to the line 2x - 3y + 18 = 0. Determine :(i) the equation of the line AP(ii) the co-ordinates of P

Th points A, B and C are (4, 0), (2, 2) and (0, 6) respectively. Find the equations of AB and BC.If AB cuts the y-axis at P and BC cuts the x-axis at Q, find the coordinates of P and Q.

The line 4x - 3y + 12 = 0 meets the x-axis at A. Write the co-ordinates of A.
Determine the equation of line through A and perpendicular to 4x - 3y + 12 = 0.

A(1, -5), B(2, 2) and C(-2, 4) are the vertices of triangle ABC. Find the equation of :
(i) the median of the triangle through A.
(ii) the altitude of the triangle through B.
(iii) the line through C and parallel to AB.

(i) Write down the equation of the line AB, through (3, 2) and perpendicular to the line 2y = 3x + 5.
(ii) AB meets the x-axis at A and the y-axis at B. Write down the co-ordinates of A and B. Calculate the area of triangle OAB, where O is the origin.

The point P is the foot of perpendicular from A(-5, 7) to the line 2x - 3y + 18 = 0. Determine :
(i) the equation of the line AP
(ii) the co-ordinates of P

Th points A, B and C are (4, 0), (2, 2) and (0, 6) respectively. Find the equations of AB and BC.
If AB cuts the y-axis at P and BC cuts the x-axis at Q, find the coordinates of P and Q.