CIE A Level Maths: Pure 1复习笔记2.1.1 Basic Coordinate Geometry
Basic Coordinate Geometry
What is basic coordinate geometry?
- Basic coordinate geometry refers to working with points, lines and shapes on the coordinate axis
- Cartesian coordinates are simply the x -y coordinate system
- Using coordinates you can
- Calculate the distance between two points (length of a line)
- Divide lines in m:n ratio,
- Find the mid-point of a line
- Calculate the area of a triangle (or other shapes)
- Find missing coordinates using any of the above
- Most of these involve working with straight line graphs
- Straight line graphs are of the form y = mx + c
- m is the gradient
- c is the y-axis intercept
- Part of a straight line is called a line segment
How do I find the length of a line (segment)?
- By finding the distance, d, between two points (x1, y1) (x2, y2)
- Pythagoras’ Theorem (a2 = b2 + c2) is used to find the length of a line
How do I find the midpoint of a line (segment)?
- M is often used as the midpoint between two points (x1, y1) (x2, y2)
- It is the average of both the x and y coordinates
Exam Tip
- Work with the square of a distance for as long as possible as this avoids early rounding errors and surds.
- Only square root when forced to or for a final answer, and use the ANS button (and other memory features) on your calculator.
Worked Example
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