What is the coordinate rule for translating left 3 and up 1?

Conditions

• The translation is defined as left 3 units and up 1 unit.

Reasoning, step by step

1. Identify the horizontal shift: left 3 units corresponds to subtracting 3 from x.
2. Identify the vertical shift: up 1 unit corresponds to adding 1 to y.
3. Combine these into the coordinate rule: $(x,y) \rightarrow (x-3, y+1)$.
4. Verify the rule with a specific point, e.g., $B(1,4)$ becomes B'(-2,5).

Example

The video derives the rule by comparing the original coordinates of point $B (1, 4)$ with its translated coordinates B' (-2, 5), observing that the x-coordinate decreases by 3 and the y-coordinate increases by 1.

Common misconceptions

• Adding 3 to x instead of subtracting 3 for a leftward shift.
• Subtracting 1 from y instead of adding 1 for an upward shift.

Watch the explanation

Explore next

• How can a translation be represented as a vector?
• How do you translate a shape on a coordinate plane?