Coordinate Geometry

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Coordinate Geometry
MyElimu Offline
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Post Icon Coordinate Geometry

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1. Distance
If A ( x1, y1) and B( x2, y2,), then distance d, from A to B = [Image: distance.jpg] 

2. Midpoint
[Image: mdpt.jpg] 


3. Gradient/Slope
[Image: grad.jpg]

4. Equation of a line
y = mx + cy - y1 = m(x - x1)

5. Parallel lines
If two lines are parallel, then they have the same gradient.

6. Perpendicular lines
If two lines are perpendicular, then the product of the gradients of the two lines is -1.or: perpendicular gradient = -1/m    where m is the gradient of the line perpendicular to it.

 7. Area of triangle
The area of the triangle formed by the three points (x1, y1), (x2, y2), (x3, y3)
[Image: area.jpg] 

8. Shoelace formula[Image: shoelace.jpg]
  • go anti-clockwise direction
  • must go back to first coordinate

9. Circle
The equation of a circle whose center is (h,k) and radius is a is given by the equation(x - h)2 + (y - k)2 = 0The equation of a circle whose centre is the origin and whose radius is a is given by the equation
x2 + y2 = a2

 The general equation of a circle is

x2 + y2 + 2gx + 2fy + c = 0

where the centre is (-g,-f) and radius is[Image: radius.jpg]
The equation of a circle whose one diameter is the line segment joining the points 
(x1, y1), (x2, y2) is given by

(x - x1)(x - x2) + (y - y1)(y - y2) = 0

Example
1. Find the equation of the line with gradient 2 passing through (1, 4).

y - 4 = 2(x - 1)
y - 4 = 2x - 2
y = 2x + 2
 

 
(This post was last modified: 02-26-2014 08:16 AM by MyElimu.)
02-26-2014 08:14 AM
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Leonard Marco Msingi Offline
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Post: #2
RE: Coordinate Geometry

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 l got u verry well.thanks
03-24-2014 11:50 PM
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