Coordinates and Straight Lines
This page introduces fundamental concepts in coordinate geometry GCSE questions and answers.
Coordinates and Gradients
The page explains how to work with coordinates and calculate gradients between two points.
Definition: The gradient between two points x1,y1 and x2,y2 is calculated using the formula: y2−y1 / x2−x1.
Example: For points −3,5 and 2,8, the gradient would be 8−5 / 2−(−3) = 3/5.
Midpoint and Distance
The concept of midpoint and distance between two points is introduced.
Highlight: The distance between two points is found using the Pythagorean theorem: √(x2−x1)2+(y2−y1)2.
Straight Line Equations
The page covers the general equation of a straight line: y = mx + c.
Vocabulary: In the equation y = mx + c, 'm' represents the gradient, and 'c' is the y-intercept.
A worked example demonstrates how to find the equation of a line parallel to y = 4x + 5 passing through the point −2,5.