Coordinate Geometry
Board: GSEB |Class:Std10
ComprehensivestudynotesforCoordinateGeometrybyAjayYadav(MathKingofKatargam).Mastereveryconceptwithclearexplanations,solvedexamples,andpracticeproblems.
TheCartesianplanehastwoperpendicularaxes:x-axis(horizontal)andy-axis(vertical).ApointPisrepresentedas(x,y)wherexistheabscissaandyistheordinate.
ThedistancebetweenpointsP(x&sub1,y&sub1)andQ(x&sub2,y&sub2)is:d=√
ThecoordinatesofpointPdividingABinratiom:nwhereA=(x&sub1,y&sub1)andB=(x&sub2,y&sub2)are:P=((mx&sub2+nx&sub1)/(m+n),(my&sub2+ny&sub1)/(m+n))forinternaldivision.
ThemidpointofABis:M=((x&sub1+x&sub2)/2,(y&sub1+y&sub2)/2).Thisisaspecialcaseofsectionformulawithm:n=1:1.
AreaofΔwithvertices(x&sub1,y&sub1),(x&sub2,y&sub2),(x&sub3,y&sub3)=(1/2)|x&sub1;(y&sub2;-y&sub3;) + x&sub2;(y&sub3;-y&sub1;) + x&sub3;(y&sub1;-y&sub2;)|.
Threepointsarecollineariftheylieonthesameline,i.e.,theareaofthetriangletheyformiszero.
| Distance | d=√ |
| Section(internal) | P=((mx&sub2+nx&sub1)/(m+n),(my&sub2+ny&sub1)/(m+n)) |
| Midpoint | M=((x&sub1+x&sub2)/2,(y&sub1+y&sub2)/2) |
| AreaofΔ | A=½|x&sub1;(y&sub2;-y&sub3;) + x&sub2;(y&sub3;-y&sub1;) + x&sub3;(y&sub1;-y&sub2;)| |
Example1:Finddistancebetween(3,4)and(0,0).
Solution:d=√
Example2:Find themidpointof(2,3)and(6,7).
Solution:M=((2+6)/2,(3+7)/2)=(4,5).
Example3:Find theareaoftrianglewithvertices(0,0),(4,0),(0,3).
Solution:Area=½|0(0-3) + 4(3-0) + 0(0-0)|=½|12| = 6 sq units.
Practice Questions
- Find the distance between A(-2, 3) and B(4, 5).
- Find the midpoint of (3, -5) and (-7, 1).
- Find the ratio in which (2, 3) divides the join of (1, 2) and (4, 5).
- Show that (1, 2), (3, 4), (5, 6) are collinear.
- Find the area of quadrilateral with vertices (1,1), (4,2), (3,5), (2,4).
Download PDF
Click here to download the PDF notes for this chapter.
Video Lessons
Watch video explanations on our Videos page.