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Coordinate Geometry CBSE NCERT Notes Class 10 Maths Chapter 7 PDF
Coordinate Geometry
Coordinate geometry has been developed as an algebraic tool for studying geometry. It helps us to study geometry using algebra, and understand algebra with the help of geometry.
Distance Formula
The distance between the points A(x1, y1) and B(x2, y2) is |AB| = √[(x2 – x1)2 + (y2 – y1)2]
Class 10 Maths Chapter 7 Examples 1:
Show that the points (1, 7), (4, 2), (–1, –1) and (– 4, 4) are the vertices of a square.
Let A(1, 7), B(4, 2), C(–1, –1) and D(– 4, 4) be the given points. Then,
Since AB = BC = CD = DA and AC = BD, all the four sides of the quadrilateral ABCD are equal and its diagonals AC and BD are also equal. Therefore, ABCD is a square.
Section Formula
The coordinate of the points dividing the line segment joining the points A(x1, y1) and B(x2, y2) internally in the ratio of m:n is
The coordinate of the points dividing the line segment joining the points A(x1, y1) and B(x2, y2) externally in the ratio of m:n is
Class 10 Maths Chapter 7 Examples 2:
Find the coordinates of the point which divides the line segment joining the points (4, –3) and (8, 5) in the ratio 3 : 1 internally.
Using the section formula, we get
Thus, (7, 3) is the required point.
Area of Triangle
The area of triangle whose coordinates are A(x1, y1), B(x2, y2) and C(x3, y3) then
Class 10 Maths Chapter 7 Examples 3:
Find the area of a triangle whose vertices are (1, –1), (– 4, 6) and (–3, –5).
Area of the triangle formed by the vertices A(1, –1), B(– 4, 6) and C (–3, –5) is
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