TOPIC 1: COORDINATE GEOMETRY ~ MATHEMATICS FORM 4
Equation of a Line
The General Equation of a Straight Line
COORDINATES OF A POINT
•The coordinates of a points – are the values of x and y enclosed by the brackets which are used to describe the position of point in a line in the plane.
- horizontal axis known as axis and
- vertical axis known as axis
Consider the xy-plane below
The coordinates of points A, B, C ,D and E are A(2, 3), B(4, 4), C(-3, -1), D(2, -4) and E(1, 0).




Exercise 1
- (3,6) and (-2,8)
- (0,6) and (99,-12)
- (4,5)and (5,4)
FINDING THE EQUATION OF A STRAIGHT LINE
The equation of a straight line can be determined if one of the following is given:-

- Gradient 2 and intercept
- Gradient and passing through the point
- Passing through the points and


The equation of a line can be expressed in two forms








Exercise 2
- Find the y-intercept of the line 3x+2y = 18 .
- What is the x-intercept of the line passing through (3,3) and (-4,9)?
- Calculate the slope of the line given by the equation x-3y= 9
- Find the equation of the straight line with a slope -4 and passing through the point (0,0).
- Find the equation of the straight line with y-intercept 5 and passing through the point (-4,8).
- By using intercepts
- By using the table of values


- Use the intercepts to plot the straight lines of the simultaneous equations
- The point where the two lines cross each other is the solution to the simultaneous equations

- y-x = 3 and 2x+y = 9
- 3x- 4y=-1 and x+y = 2
- x = 8 and 2x-3y = 10
The Coordinates of the Midpoint of a Line Segment
Determine the coordinates of the midpoint of a line segment



Therefore the coordinates of the midpoint of the line joining the points (-2,8) and (-4, -2) is (-3,3).
The Distance Between Two Points on a Plane
Calculate the distance between two points on a plane

The distance between A and B in terms of x1, y1,x2, and y2can be found as follows:Join AB and draw doted lines as shown in the figure above.
Since the triangle ABC is a right angled, then by applying Pythagoras theorem to the triangle ABC we obtain

Parallel and Perpendicular Lines

The two parallel lines must have the same slope. That is, if M1is the slope for L1and M2is the slope for L2thenM1= M2
When two straight lines intersect at right angle, we say that the lines are perpendicular lines. See an illustration below.

- α+β = 90 (complementary angles)
- α+γ= 90 (complementary angles)
- β = γ (alternate interior angles)

Generally two perpendicular lines L1and L2with slopes M1and M2respectively the product of their slopes is equal to negative one. That is M1M2= -1.
Example 10
Solution

We see that each two opposite sides of the parallelogram have equal slope.
This means that the two opposite sides are parallel to each other, which is the distinctive feature of the parallelogram. Therefore the given vertices are the vertices of a parallelogram.
Example 11 COORDINATE GEOMETRY
Right angled triangle has two sides that are perpendicular, they form 90°.We know that the slope of the line is given by: slope = change in y/change
in x

Recommended:
- TOPIC 2: AREA AND PERIMETER ~ MATHEMATICS FORM 4
- TOPIC 3: THREE DIMENSIONAL FIGURES ~ MATHEMATICS FORM 4
- TOPIC 4: PROBABILITY ~ MATHEMATICS FORM 4
- TOPIC 5: TRIGONOMETRY ~ MATHEMATICS FORM 4
- TOPIC 6: VECTORS ~ MATHEMATICS FORM 4
- TOPIC 7: MATRICES AND TRANSFORMATION ~ MATHEMATICS FORM 4
- TOPIC 8: LINEAR PROGRAMMING ~ MATHEMATICS FORM 4