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Coordinate Geometry (DP IB Applications & Interpretation (AI)): Revision Note

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Basic Coordinate Geometry

How do I find the midpoint of two points?

  • The midpoint of two points is the middle point

    • It lies on the line segment joining the two points together

    • It is the point that is equidistant from the two points

  • The coordinates of the midpoint of 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 are open parentheses fraction numerator x subscript 1 plus x subscript 2 over denominator 2 end fraction comma space fraction numerator y subscript 1 plus y subscript 2 over denominator 2 end fraction close parentheses

    • It is just the average of the two coordinates

    • This is given in the formula booklet under the prior learning section

Line graph showing line segment AB on a coordinate plane, with midpoint M. Text explains midpoint formula: M is ((x1+x2)/2, (y1+y2)/2).

How do I find the distance between two points?

  • The distance between two points is the length of the line segment joining them

  • 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 d equals square root of open parentheses x subscript 1 minus x subscript 2 close parentheses squared plus open parentheses y subscript 1 minus y subscript 2 close parentheses squared end root

    • This is just an application of Pythagoras' Theorem

    • This is given in the formula booklet under the prior learning section

  • The line segment between A and B is denoted [AB]

Examiner Tips and Tricks

It does not matter which way around you subtract the numbers because the differences are squared.

Graph with points ((x_1, y_1)) and ((x_2, y_2)), triangle formed with sides a, b, c, and Pythagorean theorem (a^2 = b^2 + c^2) demonstrated.

How do I find the gradient of the line segment between two points?

  • The gradient 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 m equals fraction numerator y subscript 2 minus y subscript 1 over denominator x subscript 2 minus x subscript 1 end fraction

    • This is change in y divided by the change in x

    • This is given in the formula booklet under the functions section

Examiner Tips and Tricks

You can switch around the coordinates in the formula fraction numerator y subscript 1 minus y subscript 2 over denominator x subscript 1 minus x subscript 2 end fraction. You just need to make sure that the first y value on the numerator and the first x value on the denominator are part of the same coordinate.

Worked Example

Point A has coordinates (3, -4) and point B has coordinates (-5, 2).

i) Calculate the distance of the line segment AB.

ai-sl-3-1-1-basic-cg-we-i

ii) Find the gradient of the line connecting points A and B.

 

ai-sl-3-1-1-basic-cg-we-ii

iii) Find the midpoint of [AB ] .

ai-sl-3-1-1-basic-cg-we-iii

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    Amber

    Author: Amber

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    Amber gained a first class degree in Mathematics & Meteorology from the University of Reading before training to become a teacher. She is passionate about teaching, having spent 8 years teaching GCSE and A Level Mathematics both in the UK and internationally. Amber loves creating bright and informative resources to help students reach their potential.

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