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Chapter 7: Coordinate Geometry

    Introduction

    Distance Between Two Points

    Distance Between Two Points on a Line Parallel To The Coordinate Axis

    Distance Between Any Two Points In the X-Y Plane

    Section Formula

    TriSectional Points of a Line

    Centroid Triangle

    Area of the Triangle

    Straight Lines

    Summary

    Enhanced Curriculum Support

    Easy Level Worksheet

    Moderate Level Worksheet

    Hard Level Worksheet

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Chapter 7: Coordinate Geometry > Summary

Summary

In this chapter, you have studied the following points :

1. The distance between P (x1,y1) and Q(x2,y2) is x2−x12+y2−y12.

2. The distance of a point P(x, y) from the is x2+y2.

3. The coordinates of the point P(x, y) which divides the line segment joining the points A(x1,y1) and B(x2,y2) internally in the ratio m1:m2 are:

(m1x2+m2x1m1+m2, m1y2+m2y1m1+m2)

4. The coordinated of the of the line segment joining the points P(x1,y1) and Q(x2,y2) is :

(x1+x22, y1+y22)

NOTE TO THE READER

We have discussed that the section formula for the coordinates (x, y) of a point P which divides internally the line segment joining the points A(x1, y1) and B(x2, y2) in the ratio m1 : m2 as follows :

x = m1x2+m2x1m1+m2

y = m1y2+m2y1m1+m2

Note that, here, PA : PB = m1 : m2.

However, if P does not lie between A and B but lies on the line AB, outside the line segment AB, and PA : PB = m1 : m2, we say that P divides externally the line segment joining the points A and B. You will study Section Formula for such case in higher classes.