Find the area of a rectangle from coordinates
When a rectangle is drawn on a coordinate grid, its area depends on its side lengths. The key idea is to find the horizontal and vertical distances between the rectangle’s vertices, then multiply them.
1. Identify the sides
- If the rectangle’s sides are parallel to the axes, one side is horizontal and the other is vertical.
- Read the coordinates of two adjacent vertices.
2. Find the lengths
- Horizontal length = difference of the x-coordinates.
- Vertical length = difference of the y-coordinates.
- Use the absolute value if needed so the length is positive.
3. Multiply to get area
area = length × width
Since the shape is a rectangle, multiplying the two side lengths gives the exact area in square units.
4. Simplify the result
If the answer is a number, write it in simplest form. If the problem involves expressions, combine like terms before giving the final area.
5. Check your work
- Make sure the two side lengths are correct and positive.
- Confirm that opposite sides match.
- If the coordinates are listed in order, the change in x and change in y should match the rectangle’s dimensions.
A good final answer is exact, simplified, and labeled with square units when appropriate.