Coordinate Geometry

MEI corse: Core 1 - Coordinate Geometry

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Section 1: Points and Straight lines

1. Draw a diagram : Does not have to be accurate, rough idea.

2. Ensure you can caluclate the gradient (m) correctly :
Gradient of a line ; m = change in y/change in x
Gradient of line joining two points ; m = (y2 - y1)/(x2 - x1)

3. Make sure you can calculate the y-intercept of a straight-line graph : y-intercept is where line crosses y-axis when x = 0.

4. Understand the equation of a straight line : y=mx+c
m=gradient
c=y-intercept.

5. Understand the conditions on the gradients of lines for the lines to be parallel or perpendicular :
Parallel - m1=m2
Perpendicular - m1 x m2 = -1

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6. Understand and remember how to calculate distance between two points :
a (squared) = b (squared) + c (squared) ie pythagoras's theorem.

7. Understand and remember how to calculate mid-point (M) :
M = (y1 + y2/ 2) or (x1 + x2/ 2)

8. Make sure you can calculate the equation of a straight line :

  • From coordinates of two points on it.
  • From its gradient and coordinates of points on it.

(y1 - y) = m(x1 - x)

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Section 2: Curves and Circles

1. Draw a diagram : helpful, rough sketch

2. Recognise standard curves

3. Make sure you know the standard circle equation :

  • General equation of a circle centre (0,0) and radius r;
    x (squared) + y (squared) = r (squared)
  • General equation of a circle centre (a,b) and radius r,
    (x - a) (squared) + (y - b) (squared) = r (squared)

4. Finding intersection of line and curve :
Solve equations simultaneously.
If its a tangent then there is a repeated root
(Quadratic equation = 0) (b (squared) -4ac = 0)

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5. Expected to know circle properties :

  • Angle in semi-circle is a right angle.
  • Perpendicular from centre of circle to a chord bisects the chord.
  • Tanget to a circle at a point is perpendicular to the radius through that point.
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Comments

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