Determine the ratio in which the line y = 2 + 3x divides the line segment AB joining the points A(-3, 9) and B(4, 2).

By two point form, Equation of line : ⇒ y - y 1 = (x - x 1 ) Equation of AB : Solving equation y = 2 + 3x and x + y = 6 simultaneously, ⇒ x + y = 6 .......(1) ⇒ y = 2 + 3x .......(2) Substituting value of y from equation (2) in (1), we get : ⇒ x + (2 + 3x) = 6 ⇒ 4x + 2 = 6 ⇒ 4x = 6 - 2 ⇒ 4x = 4 ⇒ x = ⇒ x = 1. Substituting value of x in equation (2), we get : ⇒ y = 2 + 3(1) = 2 + 3 = 5. Let (1, 5) divide the line AB in the ratio k : 1. By section formula, (x, y) = Substituting values we get : Hence, the line y = 2 + 3x divides the line segment AB in the ratio 4 : 3.

Square ABCD lies in the third quadrant of a XY plane such that its vertex A is at (-3, -1) and the diagonal DB produced is equally inclined to both the axes. The diagonals AC and BD meets at P(-2, -2). Find the :
(a) Slope of BD
(b) equation of AC

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ABCD is a rectangle where side BC is twice side AB. If △ACQ ~ △BAP, find area of △BAP : area of △ACQ.

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ABC is a triangle as shown in the figure below.
(a) Write down the coordinates of A, B and C on reflecting through the origin.
(b) Write down the coordinates of the point/s which remain invariant on reflecting the triangle ABC on the x-axis and y-axis respectively.

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Mathematics

Determine the ratio in which the line y = 2 + 3x divides the line segment AB joining the points A(-3, 9) and B(4, 2).

Section Formula

Related Questions

Square ABCD lies in the third quadrant of a XY plane such that its vertex A is at (-3, -1) and the diagonal DB produced is equally inclined to both the axes. The diagonals AC and BD meets at P(-2, -2). Find the :
(a) Slope of BD
(b) equation of AC

ABCD is a rectangle where side BC is twice side AB. If △ACQ ~ △BAP, find area of △BAP : area of △ACQ.

ABC is a triangle as shown in the figure below.
(a) Write down the coordinates of A, B and C on reflecting through the origin.
(b) Write down the coordinates of the point/s which remain invariant on reflecting the triangle ABC on the x-axis and y-axis respectively.

Mathematics

Determine the ratio in which the line y = 2 + 3x divides the line segment AB joining the points A(-3, 9) and B(4, 2).

Section Formula

Related Questions

Square ABCD lies in the third quadrant of a XY plane such that its vertex A is at (-3, -1) and the diagonal DB produced is equally inclined to both the axes. The diagonals AC and BD meets at P(-2, -2). Find the :(a) Slope of BD(b) equation of AC

ABCD is a rectangle where side BC is twice side AB. If △ACQ ~ △BAP, find area of △BAP : area of △ACQ.

ABC is a triangle as shown in the figure below.(a) Write down the coordinates of A, B and C on reflecting through the origin.(b) Write down the coordinates of the point/s which remain invariant on reflecting the triangle ABC on the x-axis and y-axis respectively.

Square ABCD lies in the third quadrant of a XY plane such that its vertex A is at (-3, -1) and the diagonal DB produced is equally inclined to both the axes. The diagonals AC and BD meets at P(-2, -2). Find the :
(a) Slope of BD
(b) equation of AC

ABC is a triangle as shown in the figure below.
(a) Write down the coordinates of A, B and C on reflecting through the origin.
(b) Write down the coordinates of the point/s which remain invariant on reflecting the triangle ABC on the x-axis and y-axis respectively.