DISPLACEMENT

Concept: Use displacement to move a figure or line from one place on a coordinate graph to another place.

Steps for Solving Displacement Problems

Step 1 | Plot the given points on a graph.
Step 2 | Connect the plotted points, forming the described figure.
Step 3 | Determine from the question if the displacement of the line or figure will be vertical or horizontal.
Step 4 | If the displacement will be vertical, all the x-coordinates will remain the same.
| If the displacement will be horizontal, all the y-coordinates will remain the same.
Step 5 | Determine from the question if the displacement of the line or figure will be in a positive or negative direction.
Step 6 | If the displacement is vertical and will be in a positive direction, the line or figure will rise on the graph by the number of units of displacement. The y-coordinate will increase by the number of units of displacement.
| If the displacement is vertical and will be in a negative direction, the line or figure will drop on the graph by the number of units of displacement. The y-coordinate will decrease by the number of units of displacement.
| If the displacement is horizontal and will be in a positive direction, the line or figure will move to the right on the graph by the number of units of displacement. The x-coordinate will increase by the number of units of displacement.
| If the displacement is horizontal and will be in a negative direction, the line or figure will move to the left on the graph by the number of units of displacement. The x-coordinate will decrease by the number of units of displacement.
Step 7 | Write the new coordinates.
Step 8 | Plot the new coordinates on a graph.
Step 9 | Connect the newly plotted coordinates, forming the newly displaced figure

Example A rectangle with coordinates A(1,-8), B(1, 2), C(0, -8) and D(0, 2) is displaced by three units upward. What are the new coordinates of the displaced triangle?

Step 1 | Plot the given points on a graph. | A (1,-8) B (1, 2) C (0, -8) D (0, 2)

-9

Step 2 | Connect the plotted points, forming the described figure. |

Step 3 | Determine from the question if the displacement of the line or figure will be vertical or horizontal. |
| Displacement will be upward, according to the problem, so it will be vertical. | vertical
Step 4 | If the displacement will be vertical, all the x-coordinates will remain the same. | A (1, ) B (1, ) C (0, ) D (0, )
| If the displacement will be horizontal, all the y-coordinates will remain the same. | Does not apply.

Step 5 | Determine from the question if the displacement of the line or figure will be in a positive or negative direction. |
| Displacement will be upward, according to the problem, so it will be positive. | positive

Step 6 | If the displacement is vertical and will be in a positive direction, the line or figure will rise on the graph by the number of units of displacement. |
| The y-coordinate will increase by the number of units of displacement. | A (1,-8) becomes (1, -5) B (1, 2) becomes (1, 5) C (0, -8) becomes (0, -5) D (0, 2) becomes (0, 5)
| If the displacement is vertical and will be in a negative direction, the line or figure will drop on the graph by the number of units of displacement. The y-coordinate will decrease by the number of units of displacement. | Does not apply.
| If the displacement is horizontal and will be in a positive direction, the line or figure will move to the right on the graph by the number of units of displacement. The x-coordinate will increase by the number of units of displacement. | Does not apply.
| If the displacement is horizontal and will be in a negative direction, the line or figure will move to the left on the graph by the number of units of displacement. The x-coordinate will decrease by the number of units of displacement. | Does not apply.

Step 7 | Write the new coordinates. | A (1, -5) B (1, 5) C (0, -5) D (0, 5)
Step 8 | Plot the new coordinates on a graph. |
Step 9 | Connect the newly plotted coordinates, forming the newly displaced figure |