(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.

Question

(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.

KnowledgeBoat · Accepted Answer

(i) Below figure shows the line AB, through (3, 2) and perpendicular to the line 2y = 3x + 5: Given, ⇒ 2y = 3x + 5 ⇒ y = Comparing above equation with y = mx + c we get, m = Let slope of line AB be m₁. Since, AB and line 2y = 3x + 5 are perpendicular. ∴ Product of their slopes will be equal to -1. ∴ m × m₁ = -1 . By point-slope form, Equation of AB : y - y₁ = m(x - x₁) ⇒ y - 2 = (x - 3) ⇒ 3(y - 2) = -2(x - 3) ⇒ 3y - 6 = -2x + 6 ⇒ 2x + 3y = 6 + 6 ⇒ 2x + 3y = 12. Hence, equation of AB is 2x + 3y = 12. (ii) Below figure shows AB with its intercepts on x axis and y axis: At A, y co-ordinate = 0 as it lies on x-axis. Substituting y = 0 in equation of AB, ⇒ 2x + 3(0) = 12 ⇒ 2x = 12 ⇒ x = 6. A = (x, 0) = (6, 0). At B, x co-ordinate = 0 as it lies on y-axis. Substituting x = 0 in equation of AB, ⇒ 2(0) + 3y = 12 ⇒ 3y = 12 ⇒ y = 4. B = (0, y) = (0, 4). Area of right angle triangle OAB = = = 12 sq. units. Hence, A = (6, 0), B = (0, 4) and area of triangle OAB = 12 sq. units.

Mathematics

(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.

Straight Line Eq

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Mathematics

(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.

Straight Line Eq

Related Questions

B(-5, 6) and D(1, 4) are the vertices of rhombus ABCD. Find the equations of diagonals BD and AC.

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.

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.

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

(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.

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.

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.

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