Today we will learn the different formulas in the Co-ordinate Geometry.
1. Distance Formula: Distance between the two points (x1, y1) and B ( x2, y2) is given by:
2. Distance of a point A (x,y) from the origin (0,0) is:
3. Internal Division: The co-ordinates of the point which divides the straight line joining two given points P (x1, y1) and Q (x2, y2) in the ratio of l : m are
4. Mid-point: The co-ordinates of the mid-point of the line joining two given points P (x1, y1) and Q (x2, y2) :
5.External Division: The co-ordinates of the point which divides the straight line joining the two given points P (x1, y1) and Q (x2, y2) externally in the ratio l: m are
6. Co-ordinates of Centroid of a Triangle: The co-ordinates of the centroid of a triangle with vertices P (x1, y1), Q (x2, y2) and R (x3, y3) are:
7. Co-ordinates of the Incentre of a Triangle: The co-ordinates of incentre of a triangle with vertices P (x1, y1) and Q (x2, y2) and R (x3, y3) and sides a, b and c are
8. Area of Triangle: The area of triangle whose vertices are A (x1, y1), B (x2, y2) and C (x3, y3)
9. This can be represented as solving the matrix:
Note: The three points P (x1, y1), Q (x2, y2) and R (x3, y3) are collinear if the area of the triangle is zero i.e. 1/2[x1(y2 - y3) - x2(y1 - y3) + x3(y1 - y2) = 0.
10. The equation of x-axis is y = 0
11.The equation of y-axis is x = 0
12.The equation of a straight line parallel to y-axis at a distance ‘a’ units from it, is x = a
13.The equation of a straight line parallel to x-axis at distance ‘b’ units from it, is y = b
14.The equation of a straight line passing through the origin (0,0) is y = mx, where m = tan θ and θ is the angle measured in the anti-clockwise direction from the positive direction of x-axis to the upper part of the line.
15. The general form of the equation is y = mx + c where m = tan θ, θ is the angle formed by x-axis and c is the intercept on the y-axis.
(a) If c = 0, the straight line passes through the origin and makes an angle θ with the x-axis i.e. y = mx.
(b) If m = 0, the line is parallel to x-axis and the equation of such a line takes the form y = c
(c) If θ = 90°, the line is parallel to the y-axis.
16. Intercept Form: x/a +y/b = 1
17. Point-Slope Form: y - y1 = m(x -x1).
18. Two-Point Form : 
19. Length of perpendicular from a point (x1, y1) to the line ax + by + c = 0 is:
20. The general equation of line is ax + by + c = 0.
(1) The equation of a line parallel to ax + by + c = 0 is ax + by + k = 0
(2) The equation of a line perpendicular to ax + by + c = 0 is bx - ay + k = 0
21. Two lines are parallel if their slopes are equal. Two lines are perpendicular if the product of their slopes is -1, hence two lines with slopes m1 and m2 are perpendicular if m1m2 = -1.
21. Angle θ between two lines y = m1x + c1 and y = m2x + c2 is given by tan θ =
22. Two lines y = a1x + b1y + c1 and y = a2x + b2y + c2 are:
(1) Parallel, if a1/a2 = b1/b2 ≠ c1/c2
(2) Perpendicular, if a1a2 + b1b2 = 0
(3) Co-incident, if a1/a2 = b1/b2 = c1/c2
(4)Intersecting, if they are neither coincident nor parallel.
23. The equation of a circle with centre (0,0) and radius r is given by x² + y² = r²
24.The equation of a circle with centre (h, k) and radius r is given by (x - h)² + ( y - k)² = r²
25. The equation of tangent to a circle x² + y² = r², at a point (x1,y1) is xx1 + yy1 = r²
Thanks!
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