Topics covered within this unit: 31·1 Midpoint of a line segment
31·2 Length of a line segment (distance between two points)
31·3 Slope of the line 31·4 Equation of a line
31·5 Working with the equation of a line
31·6 Graphing lines when given the equation of the line
31·7 Point of intersection of two lines (simultaneous equations)
The Learning Outcomes covered in this unit are contained in the following sections:
GT.5 GT.6 AF.4c GT.3a GT.3b 31·1 Midpoint of a line segment
Key words Midpoint
y- intercept Collinear points
By the end of this section you should: ● recall how to label and plot coordinates on a coordinate (Cartesian) plane ● recall the defi nition of a line segment
● understand and be able to calculate the coordinates of the midpoint of a line segment
Working with the coordinate plane
Something to think about …
You are playing an online game in which you are navigating a battleship.
Your mission is to lay mines at the points where the enemy travel lanes intersect.
The enemy travel lanes are represented by the following equations. Lane 1: x − y = − 4 Lane 2: 5x − y = 8 Lane 3: x − 2y = − 2
At what three points should you lay your mines?
y
4 3 2 1
–1 0 –1
1 A = (2, 3)
In Section A, Unit 1, we introduced the Cartesian (coordinate) plane. We learned that it consists of an x -axis (horizontal line) and a y -axis (vertical line).
2 3 x
We learned that to label or plot a location on the coordinate plane, we use two coordinates (numbers) on the grid, which are written in the form ( x, y ). The x -coordinate represents the horizontal position and the y -coordinate represents the vertical position.
The point (2, 3) shown has an x -coordinate of 2 and a y -coordinate of 3.