A Level 2017: Chapter 5 Coordinate Geometry

Nicola Trubridge, Oct 8, 2017

Table of Contents

  1. Midpoints
    1. The midpoint of two points
    2. Midpoint Coordinates (II)
  2. Distance between points
    1. The distance between two points
  3. Gradients
    1. The gradient of a line joining two points
  4. Parallel and perpendicular
    1. Parallel lines
    2. Perpendicular lines
    3. Parallel & Perpendicular Lines
    4. Exploring parallel and perpendicular lines
  5. Equation of a line
    1. The form y = mx + c
    2. The form ax + by + c = 0
    3. Equation of a line from gradient and a point
  6. Circles
    1. Circles
  7. Circle Properties
    1. Tangent and radius
    2. Angle in a semicircle
    3. Perpendicular to chord

1.

Midpoints

  • 1. The midpoint of two points
  • 2. Midpoint Coordinates (II)

1.1.

The midpoint of two points

Use the checkbox to see how you can find the midpoint.[br]You can move the two points.
– Nicola Trubridge, Integral Resources

1.2.

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2.

Distance between points

  • 1. The distance between two points

2.1.

The distance between two points

Use the checkbox to see how Pythagoras' theorem is used to find the distance between two points.[br]You can move the two points.
– Integral Resources

3.

Gradients

  • 1. The gradient of a line joining two points

3.1.

The gradient of a line joining two points

Use the checkbox to see how you can find the gradient of the line joining the two points.[br]You can move the two points.
– Integral Resources

4.

Parallel and perpendicular

  • 1. Parallel lines
  • 2. Perpendicular lines
  • 3. Parallel & Perpendicular Lines
  • 4. Exploring parallel and perpendicular lines

4.1.

Parallel lines

You can change the blue line by moving either of the green points.[br]The red line is parallel to the blue line. What do you notice about the gradients and the equations of the lines?
– Integral Resources

4.2.

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4.3.

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4.4.

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5.

Equation of a line

  • 1. The form y = mx + c
  • 2. The form ax + by + c = 0
  • 3. Equation of a line from gradient and a point

5.1.

The form y = mx + c

Use the sliders to set the values of m and c, and then use the checkbox to see the line.[br]What is the significance of the values of m and c?
The form y = mx + c
– Integral Resources

5.2.

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5.3.

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6.

Circles

  • 1. Circles

6.1.

Circles

Change the values of [math]a[/math], [math]b[/math] and [math]r[/math] to see different circles. Write down the centre and radius for each circle. How can you predict the centre and radius from the equation of the circle?[br][br]Use the checkbox to show a triangle on the circle. Write down expressions in terms of [math]a[/math], [math]b[/math] and [math]r[/math] for the length of each side. How does this explain the equation of the circle?
– Nicola Trubridge, Integral Resources

7.

Circle Properties

  • 1. Tangent and radius
  • 2. Angle in a semicircle
  • 3. Perpendicular to chord

7.1.

Tangent and radius

A tangent to a circle at a point is perpendicular to the radius of the circle at that point.[br]Move the point P around the circle to see that the tangent is always perpendicular to the radius.
This construction [i]demonstrates[/i] this circle theorem, but it does not [i]prove[/i] it. Try to prove the theorem.
– Nicola Trubridge, Integral Resources

7.2.

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7.3.

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