Coordinate Geometry

1. Coordinates of a point

1.1. The coordinates of a point are a pair of numbers that define its exact location on a two-dimensional plane. The coordinates of a given point represent how far along each axis the point is located.

2. Length of line segment

3. Graphs of straight lines

3.1. When drawing the graph of a straight line, one must remember the equation of the line - y = mx + c. m refers to the gradient of the line i.e., the steepness of the line. c is the y-intercept, where the line cuts the y-axis. Choose three points by substituting values of x into the equation. Generally the 3 values of x are x = 0, negative value of x and positive value of x.

3.2. There are four graphs of straight lines, due to differing gradients.

3.2.1. 1. negative gradient

3.2.2. 2. positive gradient

3.2.3. 3. gradient = 0

3.2.4. 4. gradient undefined

4. Gradient of a straight line

4.1. choose any two points on the line. draw a right-angled triangle with the line as hypotenuse. use the scale on each axis to find the triangle's: vertical length. horizontal length. work out the vertical length ÷ horizontal length. the result is the gradient of the line.

5. Find equation of a straight line

5.1. The general equation of a straight line is y = mx + c, where m is the gradient, and y = c is the value where the line cuts the y-axis. This number c is called the intercept on the y-axis.

6. Coordinates of point of intersection of 2 lines

6.1. Coordinates of a point at which two lines intersect.

6.2. Firstly, we need the equations of the two lines. If you do not have the equations: Equation of a line - slope/intercept form and Equation of a line - point/slope form

6.3. Then, since at the point of intersection, the two equations will have the same values of x and y, we set the two equations equal to each other. This gives an equation that we can solve for x

6.4. We substitute that x value in one of the line equations and solve it for y.

6.5. (5,-2) is the coordinate of intersection of these two lines.