6240 WordsFeb 28, 201325 Pages

CO-ORDINATE GEOMETRY
1 To change from Cartesian coordinates to polar coordinates, for X write r cos θ and for y write r sin θ . Write y and for tan θ x2 x1 y2
2
To change from polar coordinates to cartesian coordinates, for r2 write X2 + y2 ; for r cos θ write X, for r sin θ write .
.
3 Distance between two points (X1, Y1 ) and (X2 , Y2 ) is y1
4
5 Distance between (r1 , θ 1 ) and (r2 , θ2 ) is 6 r
Distance of ( x1 , y1 ) from the origin is x
2 2 r 2 r1 r2 cos θ2 θ1 1 2 Coordinates of the point which divides the line joining (X1 , Y1 ) and , ( m1 + m2
2 1
y
2 1
(X2, Y2 ) internally in the ratio m1 : m2 are :0)
7. Coordinates of the point which divides the line joining (X1 , Y1 ) and (X2 ,Y2 ) externally in the ratio m1 : m2 are :, (m1 – m2 0)
8. Coordinates of the mid-point (point which bisects) of the seg. Joining (X1, y1) and (X2 y2 ) are :
, 9. (a) Centriod is the point of intersection of the medians of triangle. (b) In-centre is the point of intersection of the bisectors of the angles of the triangle. (c) Circumcentre is the point of intersection of the right (perpendicular) bisectors of the sides of a triangle. (d) Orthocentre is the point of intersection of the altitudes (perpendicular drawn from the vertex on the opposite sides) of a triangle. 10.Coordinates of the centriod of the triangle whose vertices are (x1 , y1 ) ; (x2 , y2 ) ; ( x3 , y3 ) are
11. Coordinates of the in-centre of the triangle whose vertices are A (x1 ,y1) ; B (x2 ,y2 , ) ; C (x3 ,y3 ) and 1 (BC ) c. are . a, 1 (CA) b, 1 (AB)
12 Slope of line joining two points (x1 ,y1) and (x2 ,y2 )is m 13. Slope of a line is the tangent ratio of the angle which the line makes with the positive direction of the x-axis. i.e. m tan θ
14. Slope of the perpendicular to x-axis (parallel to y –axis) does not exist, and the slope of line parallel to x-axis

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