Review the key concepts, formulae, and examples before starting your quiz.
🔑Concepts
Coordinates: A pair of numbers (x, y) used to describe the exact position of a point on a grid.
The x-axis: The horizontal line at the bottom of the grid (always read this first).
The y-axis: The vertical line on the side of the grid (read this second).
The Origin: The point where the x-axis and y-axis meet, represented by the coordinates (0, 0).
Translation: Moving a shape or point from one position to another without turning it or changing its size.
Describing Movement: Movement is described in terms of 'units left/right' and 'units up/down'.
📐Formulae
Coordinate Notation: (Remember: 'Along the corridor and up the stairs')
Horizontal Change (Right):
Horizontal Change (Left):
Vertical Change (Up):
Vertical Change (Down):
💡Examples
Problem 1:
A point is located at (2, 3). If you move the point 4 units to the right and 1 unit down, what are the new coordinates?
Solution:
(6, 2)
Explanation:
Starting at x=2, moving 4 units right means adding: . Starting at y=3, moving 1 unit down means subtracting: . The new position is (6, 2).
Problem 2:
Describe the movement required to get from point A (1, 5) to point B (4, 5).
Solution:
3 units to the right.
Explanation:
Compare the x-coordinates: units movement to the right. The y-coordinates are the same (5), so there is no vertical movement.
Problem 3:
A square has a vertex at (1, 1). If the square is moved '2 units left and 3 units up', where is the new vertex?
Solution:
The coordinate cannot be plotted on a standard positive-only quadrant if it goes below zero, but mathematically it is (-1, 4).
Explanation:
Subtract 2 from the x-coordinate () and add 3 to the y-coordinate ().