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Coordinate Geometry (Cambridge (CIE) IGCSE Maths)

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  • FrontCoordinates

    True or False?

    On a coordinate grid, the point which is 3 units right and 4 units up from the origin has coordinates (3,4).

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  • True or False?

    On a coordinate grid, the point which is 3 units right and 4 units up from the origin has coordinates (3,4).

    True.

    On a coordinate grid, the point which is 3 units right and 4 units up from the origin has coordinates (3,4).

  • Which coordinates would be a units left and b units down from the point open parentheses x comma space y close parentheses?

    The coordinates a units left and b units down from the point open parentheses x comma space y close parentheses would be open parentheses x minus a comma space y minus b close parentheses.

  • State an expression for the coordinates of the midpoint between open parentheses x subscript 1 comma space y subscript 1 close parentheses and open parentheses x subscript 2 comma space y subscript 2 close parentheses.

    The midpoint between open parentheses x subscript 1 comma space y subscript 1 close parentheses and open parentheses x subscript 2 comma space y subscript 2 close parentheses is given by the expression open parentheses fraction numerator x subscript 1 plus x subscript 2 over denominator 2 end fraction comma fraction numerator y subscript 1 plus y subscript 2 over denominator 2 end fraction close parentheses.

  • True or False?

    The x-coordinate of the midpoint is equal to the mean of the x-coordinates of the two points.

    True.

    The x-coordinate of the midpoint is equal to the mean of the x-coordinates of the two points.

    The y-coordinate of the midpoint is also equal to the mean of the y-coordinates of the two points.

  • What does the gradient of a line measure?

    The gradient of a line measures the steepness of the line.

  • True or False?

    A line with a gradient of -4 is steeper than a line with a gradient of -5.

    False.

    A line with a gradient of -5 is steeper than a line with a gradient of -4. The steeper line is the one with the bigger gradient value when you ignore negative signs.

  • True or False?

    The gradient of a line is equal to fraction numerator change space in space y over denominator change space in space x end fraction.

    True.

    The gradient of a line is equal to fraction numerator change space in space y over denominator change space in space x end fraction.

  • State the formula for the gradient of the line that passes through open parentheses x subscript 1 comma y subscript 1 close parentheses and open parentheses x subscript 2 comma y subscript 2 close parentheses.

    The formula for the gradient of the line that passes through open parentheses x subscript 1 comma y subscript 1 close parentheses and open parentheses x subscript 2 comma y subscript 2 close parentheses is m equals fraction numerator y subscript 2 minus y subscript 1 over denominator x subscript 2 minus x subscript 1 end fraction.

    The formula m equals fraction numerator y subscript 1 minus y subscript 2 over denominator x subscript 1 minus x subscript 2 end fraction will also give the gradient.

  • True or False?

    A positive gradient means the line goes upwards from bottom left to top right.

    True.

    A positive gradient means the line goes upwards from bottom left to top right.

  • True or False?

    The gradient of the line which passes through open parentheses 4 comma space 5 close parentheses and open parentheses 1 comma space 2 close parentheses can be found by calculating fraction numerator 2 minus 5 over denominator 4 minus 1 end fraction.

    False.

    The gradient of the line which passes through open parentheses 4 comma space 5 close parentheses and open parentheses 1 comma space 2 close parentheses can not be found by calculating fraction numerator 2 minus 5 over denominator 4 minus 1 end fraction.

    The order needs to be consistent. If the second coordinate is used first for the y coordinates, then the second coordinate should be used first for the x coordinates.

    It should be either fraction numerator 2 minus 5 over denominator 1 minus 4 end fraction or fraction numerator 5 minus 2 over denominator 4 minus 1 end fraction.

  • State the formula for the length of the line segment between open parentheses x subscript 1 comma space y subscript 1 close parentheses and open parentheses x subscript 2 comma space y subscript 2 close parentheses.

    The formula for the length of the line segment between open parentheses x subscript 1 comma space y subscript 1 close parentheses and open parentheses x subscript 2 comma space y subscript 2 close parentheses is square root of open parentheses x subscript 2 minus x subscript 1 close parentheses squared plus open parentheses y subscript 2 minus y subscript 1 close parentheses squared end root.

    This is just using Pythagoras' theorem on the line segment between the two points.

  • True or False?

    The length of the line segment between open parentheses 4 comma space minus 1 close parentheses and open parentheses 7 comma space 6 close parentheses can be found by calculating square root of open parentheses 4 minus open parentheses negative 1 close parentheses close parentheses squared plus open parentheses 7 minus 6 close parentheses squared end root.

    False.

    The length of the line segment between open parentheses 4 comma space minus 1 close parentheses and open parentheses 7 comma space 6 close parentheses can not be found by calculating square root of open parentheses 4 minus open parentheses negative 1 close parentheses close parentheses squared plus open parentheses 7 minus 6 close parentheses squared end root. Each bracket should be the difference between the x values or the y values.

    It should be square root of open parentheses 7 minus 4 close parentheses squared plus open parentheses 6 minus open parentheses negative 1 close parentheses close parentheses squared end root.

Previous:ProportionNext:Linear Graphs

    1. Topic 1

      Number Toolkit

    2. Topic 2

      Set Notation & Venn Diagrams

    3. Topic 3

      Prime Factors, HCF & LCM

    4. Topic 4

      Powers, Roots & Standard Form

    5. Topic 5

      Fractions Toolkit

    6. Topic 6

      Percentages Toolkit

    7. Topic 7

      Simple & Compound Interest, Growth & Decay

    8. Topic 8

      Surds

    9. Topic 9

      Working with FDP

    10. Topic 10

      Working with Ratios

    11. Topic 11

      Compound Measures (Speed, Density, Pressure)

    12. Topic 12

      Time, Currency & Conversions

    13. Topic 13

      Rounding, Estimation & Bounds

    14. Topic 14

      Using a Calculator

    1. Topic 1

      Algebra Toolkit

    2. Topic 2

      Algebraic Roots & Indices

    3. Topic 3

      Expanding & Factorising Brackets

    4. Topic 4

      Linear Equations & Inequalities

    5. Topic 5

      Quadratic Equations

    6. Topic 6

      Rearranging Formulas

    7. Topic 7

      Simultaneous Equations

    8. Topic 8

      Algebraic Fractions

    9. Topic 9

      Forming & Solving Equations

    10. Topic 10

      Functions

    11. Topic 11

      Sequences

    12. Topic 12

      Proportion

    1. Topic 1

      Coordinate Geometry

    2. Topic 2

      Linear Graphs

    3. Topic 3

      Quadratic Graphs

    4. Topic 4

      Further Graphs & Tangents

    5. Topic 5

      Solving & Graphing Inequalities

    6. Topic 6

      Real-Life Graphs

    7. Topic 7

      Differentiation

    1. Topic 1

      Geometry Toolkit

    2. Topic 2

      Angles in Polygons & Parallel Lines

    3. Topic 3

      Bearings, Constructions & Scale Drawings

    4. Topic 4

      Circle Theorems

    1. Topic 1

      Area & Perimeter

    2. Topic 2

      Circles, Arcs & Sectors

    3. Topic 3

      Volume & Surface Area

    4. Topic 4

      Congruence & Similarity

    1. Topic 1

      Right-Angled Triangles (Pythagoras & Trigonometry)

    2. Topic 2

      Sine, Cosine Rule & Area of Triangles

    3. Topic 3

      3D Pythagoras & Trigonometry

    4. Topic 4

      Trigonometric Graphs & Equations

    1. Topic 1

      Vectors

    2. Topic 2

      Transformations

    1. Topic 1

      Basic Probability

    2. Topic 2

      Probability Diagrams (Tree & Venn Diagrams)

    3. Topic 3

      Conditional Probability

    1. Topic 1

      Averages & Range

    2. Topic 2

      Statistical Diagrams

    3. Topic 3

      Histograms

    4. Topic 4

      Cumulative Frequency

    5. Topic 5

      Scatter Graphs & Correlation