Coordinate Geometry and the straight line

1
Coordinate Geometry and the straight line

• At the end of this chapter you should know
• Equations of straight lines
• How to find the equation of a straight line
  through two given points
• How to find the equation of a straight line
  through a given point, with a gradient
• What happen with the gradient when lines are
  parallel and perpendicular

2
Standard form Straight line

gradient
y-intercept
easieteach P5
3
The length of a line segment

• AB is a line segment

Pythagoras theorem
(5, 6)
B
Vertical distance
y2 y1 6 1 5
5
3
Horizontal distance
A
(2, 1)
x2 x1 5 2 3
4
Find the length of the line segment AB

5
Prove that triangle ABC is isosceles

sketch
AB AC
length?
6
The midpoint of a line segment

coordinate of M
Arithmetic mean
(8, 11)
B
M
A
(2, 1)
M (5, 6)
7
Find the midpoint of the line segment AB

8

Ex 6A page 96 1 A - C 2 A - C 4 11
9
The gradient of a line

controls the steepness of the line
(4, -5)
B
A
(2, -1)
10
Parallel and Perpendicular lines
easieteach P6


Find the gradient of the line parallel to
Find the gradient of the line perpendicular to
11
Find the gradient perpendicular to line AB

12

Ex 6B page 105 1 A - C 2 3
13
Plenary

easieteach P7 8