Coordinate Geometry

7.4.2 Equation of Straight Lines Case 1 1. The gradient and coordinates of a point are given. 2. The equation of a straight line with gradient m passes through the point (x1, y1) is: Example 1: A straight line with gradient –3 passes through the point (–1, 5). Find the equation of this line. Solution: y – y1 … Read more

7.4.1 Axes Intercepts and Gradient (A) Formula for gradient: 1. Gradient of the line joining (x1, yl) and (x2, y2) is: 2. Gradient of the line with knowing x–intercept and y–intercept is: 3. The gradient of the straight line joining P and Q is equal to the tangent of angle θ, where θ is the angle … Read more

7.3 Areas of Polygons (A) Area of Triangle Area of Triangle 1. When the given points are taken in an anticlockwise direction the result is positive; taken in a clockwise direction the result is negative. The answer for the area must be given as a positive value. Example 1: Calculate the area of ∆ ABC with … Read more

7.2 Division of a Line Segment (A) Midpoints of a Line Segment Formula for the midpoint, M of A (xl, y1) and B (x2, y2) is Example 1: Given B (m – 4, 3) is the midpoint of the straight line joining A(–1, n) and C (5, 8). Find the values of m and n. Solution: B  is the midpoint of  A … Read more

7.1 Distance between Two Points A (x1, y1) and C (x2, y2) are two points on a coordinate plane as shown below. BC is parallel to the x-axis and AB is parallel to the y-axis.  Hence  ∆ ABC = 90°. Distance between Point A and C =   Example: Find the distance between the points P (2, –2) and Q … Read more