# Lesson Notes By Weeks and Term - Senior Secondary School 3

Coordinate Geometry of straight line: Cartesian coordinate graphs

SUBJECT: MATHEMATICS

CLASS:  SS 3

DATE:

TERM: 2nd TERM

REFERENCE TEXT

• New General Mathematics for SS book 3 by J.B Channon
• Essential Mathematics for SS book 3
• Mathematics Exam Focus
• Waec and Jamb past Questions

WEEK TWO

TOPIC: Coordinate Geometry of straight line: Cartesian coordinate graphs

• Coordinate Geometry of straight line: Cartesian coordinate graphs
• distance between two points
• midpoint of the line joining two points
• Coordinate Geometry of Straight line:
• Cartesian coordinate graph:

Distance between two lines:

In the figure below, the coordinates of the points A and B are (x1, y1) and (x2, y2), respectively. Let the length of AB be l.

y

B(x2, y2)

l

y2 – y1

A(x1, y1)      x2 – x2          C

X

Using Pythagoras theorem:

AB2 = AC2 + BC2

l2 =(x2 – x1)2 + (y2 – y1)2

l  = √(x2 – x1)2 + (y2 – y1)2

Example:

Find the distance between the each pair of points: a. (3, 4) and (1, 2)   b. (3, - 3) and (- 2, 5)

Solution:

Using l =√(x2 – x1)2 + (y2 – y1)2

1. l = √(3 – 1)2 + (4 – 2)2

l = √22 + 22

l = √8 = 2√2 units

1. l = √(3 – (-2)2 + (-3 – 5)2

=  √52 + (-8)2

=  √25 + 64 = √89 = 9.43 units

Evaluation: Find the distance between the points in each of the following pairs leaving your answers in surd form:  1. (-2, - 5) and (3, - 6)     2. (- 3, 4) and (- 1, 2)

Mid-point of a line:

The mid-point of the line joining two points:

y

B(x2, y2)

y2 - y

M(x, y)                         D

x2 –x

y – y1

A(x1, y1)   x – x1      N                      C

X

Triangle MAN and BMD are congruent, so AM = MD and BD = MN

x – x1 = x2 – x                                          y – y1 = y2 – y

x + x = x2 + x1                                          y + y = y2 + y1

2x = x2 + x1                                          2y      = y2 + y1

x= x2 + x1                                                  y = y2 + y1

2                                                                    2

Hence, the mid-point of a straight line joining two is    x2 + x1  ,y2 + y1

2                 2

Example: Find the coordinates of the mid-point of the line joining the following pairs of points.

1. (3, 4) and (1, 2)         b. (2, 5) and ( - 3, 6)

Solution:

Mid-point =         x2 + x1  ,y2 + y1

2                2

1. Mid-point =  1 + 3  ,     4 + 2       =  (2, 3)

2               2

1. Mid-point =  - 3 + 2  ,   6+ 5       =   - 1  ,   11

2             2                  2       2

Evaluation: Find the coordinates of the mid-point of the line joining the following pairs of points.

1. (- 2 , - 5) and (3, - 6)         b. (3, 4) and ( - 1, - 2)

General Evaluation

1. Find the distance between the points in each of the following pairs leaving your answers     in surd form:  1. (7, 2) and (1, 6)
2. What is the value of r if the distance between the points (4, 2) and (1, r) is 3 units?
3. Find the coordinates of the mid-point (-3, -2) and (-7, - 4)

Reading Assignment: NGM for SS 3 Chapter 9 page 77 – 78,

Weekend Assignment:

1. Find the value of α2 + β2 if α + β = 2 and the distance between the points (1, α) and (β, 1) is 3 units.
2. The vertices of the triangle ABC are A (7, 7), B (- 4, 3) and C (2, - 5). Calculate the length of the longest side of triangle ABC.
3. Using the information in ‘2’ above, calculate the line AM, where M is the mid-point of the side opposite A.