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Business Mathematics and Basic Statistics · Class 12 Commerce

Ch 5Coordinate Geometry (Two Dimensions) — Class 12 Business Mathematics and Basic Statistics, concept-first.

Business problems that involve two related quantities — for example, the price of a share plotted against time, or a firm’s total cost plotted against the number of units produced — are easiest to study with a picture.

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Concepts

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Unit weightage

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Key concepts

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The Cartesian Coordinate System

The Cartesian coordinate system fixes a point in a plane using an ordered pair , measured from two perpendicular axes crossing at the origin .

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Chapter contents

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1

The Cartesian Coordinate System

Business problems that involve two related quantities — for example, the price of a share plotted against time, or a firm’s total cost plotted against the number of units produced — are easiest to stu…

2

Distance Between Two Points

Suppose two branches of a business, or two stops on a delivery route, sit at points and on the coordinate plane.

3

Section Formula (Internal Division)

Often what is needed is not the distance between two points but a point that lies between them in a stated proportion — for instance, a warehouse located one-third of the way from a firm’s old depot t…

4

Centroid of a Triangle

A triangle’s median is the line segment joining one vertex to the mid-point of the opposite side; every triangle has three medians, one from each vertex.

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14 Q
+Show 8 questions8 questions
  1. Example 1State the quadrant, or the axis, in which each of the following points lies: (i) $(5, -2)$ (ii) $(-3, -7)$ (iii) $(0, 4)$ (iv) $(-6, 3)$.Free
  2. Example 2Find the distance between the points $P(3, 2)$ and $Q(7, 5)$.Free
  3. Example 3Show that the points $A(4, 3)$, $B(-4, 3)$ and $C(0, -3)$ are the vertices of an isosceles triangle.Free
  4. Example 4Using the distance formula, show that the points $A(1, 2)$, $B(3, 8)$ and $C(4, 11)$ are collinear.Preview
  5. Example 5Find the coordinates of the point which divides the line segment joining $A(1, 2)$ and $B(7, 8)$ internally in the ratio $1:2$.Preview
  6. Example 6Find the mid-point of the line segment joining the points $(-3, 5)$ and $(7, -1)$.Preview
  7. Example 7Find the centroid of the triangle whose vertices are $A(2, 3)$, $B(4, 7)$ and $C(6, -1)$.Preview
  8. Example 8Two vertices of a triangle are $A(3, -2)$ and $B(-1, 4)$. If the centroid of the triangle is $G(2, 3)$, find the third vertex $C$.Preview
+Show 6 questions6 questions
  1. Q9Find the distance between the points $(-2, -3)$ and $(2, 0)$.Free
  2. Q10Using the distance formula, show that the points $A(0, 0)$, $B(5, 0)$ and $C(5, 12)$ form a right-angled triangle.Free
  3. Q11Find the coordinates of the point dividing the line segment joining $(2, -1)$ and $(8, 5)$ internally in the ratio $2:1$.Preview
  4. Q12Find the point which divides the line segment joining $A(-4, 1)$ and $B(2, -3)$ internally in the ratio $3:2$.Preview
  5. Q13Find the centroid of the triangle with vertices $(-3, -1)$, $(2, 5)$ and $(7, -4)$.Preview
  6. Q14Using the distance formula, examine whether the points $(1, 1)$, $(2, 3)$ and $(4, 7)$ lie on a straight line.Preview