Notes for coordinate geometry chapter of class 10 Mathematics. Dronstudy provides free comprehensive chapterwise class 10 Mathematics notes with proper images & diagram.
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(1) The abscissa and ordinate of a given point are the distances of the point from y-axis and x-axis respectively.
(2) The coordinates of any point on x-axis are of the form (x,0).
(3) The coordinates of any point on y-axis are of the form (0,y).
(4) The distance between points and is given by,
For Example:
If and , then distance between these two point is given as follow:
Here, ,
, Â
Let O be the distance between two points and .
The distance between two point is given by
Â
Hence the distance between two points is 13 units.
(5) Distance of a point from the origin is given byÂ
For Example:Â and is given then distance between them i.e. is calculated as follow:
(6) The coordinates of the point which divides the join of points and internally in the ration m:n areÂ
For Example:Â Find the coordinates of the point which is divided the line segment joining (-1,3) and (4,-7) internally in the ratio 3:4.
Solution:Â Let the end points of AB be A(-1, 3) and B(4, -7).
(, ) and (, )
Also, and
Let be the required point, then by section formula, we have ,
Â Â Â Â Â Â Â Â Â Â Â ,
Â Â Â Â Â Â Â Â Â Â Â ,
Â Â Â Â Â Â Â Â Â Â Â ,
Hence, the required point is
(7) The coordinates of the mid-point of the line segment joining the points and are .
For Example:Â and
So mid-point of is .
(8) The coordinates of the centroid of triangle formed by the points , and areÂ
For Example:Â Find centroid of triangle whose vertices are , ,
Solution:Â We know that the coordinates of the centroid of a triangle whose angular points are , and are
So, the coordinates of the centroid of a triangle whose vertices are , and are
(9) The are of triangle formed by the points , and isÂ Â Or,
For Example:Â Find area of triangle whose vertices are , ,
Solution:Â Let , and be the given points
Area of
Â
(10) If points , and are collinear, then
For Example:Â Let , and be the given points.
Three points are collinear if area enclosed by three points is zero.
Area of
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