In what ratio is the segment joining the points A(6, 5) and B(-3, 2) divided by the y-axis? Find the point at which the y-axis cuts AB.
Section Formula
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Question

In what ratio is the segment joining the points A(6, 5) and B(-3, 2) divided by the y-axis? Find the point at which the y-axis cuts AB.

KnowledgeBoat · Accepted Answer

When a point lies on the y-axis, its x-coordinate is always 0. Let the point where the y-axis cuts AB be P(0, y). Let ratio in which P divides AB be m1 : m2. By section-formula, x = Substituting values we get : Thus, m1 : m2 = 2 : 1. By section-formula, y = Substitute values we get: P = (0, y) = (0, 3). Hence, AB is divided in ratio 2 : 1 and point at which the y-axis cuts AB is (0, 3).

Mathematics

In what ratio is the segment joining the points A(6, 5) and B(-3, 2) divided by the y-axis? Find the point at which the y-axis cuts AB.

Section Formula

Related Questions

In what ratio does the point P(a, -1) divide the join of A(1, -3) and B(6, 2)? Hence, find the value of a.

The line segment joining A(2, 3) and B(6, -5) is intercepted by the x-axis at the point k. Find the ratio in which k divides AB. Also, write the co-ordinates of the point k.

(i) Write down the co-ordinates of the point P that divides the line segment joining A(-4, 1) and B(17, 10) in the ratio 1 : 2.
(ii) Calculate the distance OP, where O is the origin.
(iii) In what ratio does the y-axis divide the line AB?

The line segment joining P(-4, 5) and Q(3, 2) intersects the y-axis at R. PM and QN are perpendiculars from P and Q on the x-axis. Find :
(i) the ratio PR : RQ
(ii) the coordinates of R.
(iii) the area of quadrilateral PMNQ.

Mathematics

In what ratio is the segment joining the points A(6, 5) and B(-3, 2) divided by the y-axis? Find the point at which the y-axis cuts AB.

Section Formula

Related Questions

In what ratio does the point P(a, -1) divide the join of A(1, -3) and B(6, 2)? Hence, find the value of a.

The line segment joining A(2, 3) and B(6, -5) is intercepted by the x-axis at the point k. Find the ratio in which k divides AB. Also, write the co-ordinates of the point k.

(i) Write down the co-ordinates of the point P that divides the line segment joining A(-4, 1) and B(17, 10) in the ratio 1 : 2.(ii) Calculate the distance OP, where O is the origin.(iii) In what ratio does the y-axis divide the line AB?

The line segment joining P(-4, 5) and Q(3, 2) intersects the y-axis at R. PM and QN are perpendiculars from P and Q on the x-axis. Find :(i) the ratio PR : RQ(ii) the coordinates of R.(iii) the area of quadrilateral PMNQ.

(i) Write down the co-ordinates of the point P that divides the line segment joining A(-4, 1) and B(17, 10) in the ratio 1 : 2.
(ii) Calculate the distance OP, where O is the origin.
(iii) In what ratio does the y-axis divide the line AB?

The line segment joining P(-4, 5) and Q(3, 2) intersects the y-axis at R. PM and QN are perpendiculars from P and Q on the x-axis. Find :
(i) the ratio PR : RQ
(ii) the coordinates of R.
(iii) the area of quadrilateral PMNQ.