A rectangle has been drawn on a coordinate grid. How can you use the given coordinates to work out the coordinates of the other three vertices?

The given vertex is $(5,4)$. From the grid, the rectangle spans from $x=2$ to $x=5$ and from $y=2$ to $y=4$. This means its width is $5-2=3$ units and its height is $4-2=2$ units.

Since one vertex is $(5,4)$, the other vertices can be found by moving 3 units horizontally and 2 units vertically.
The other three vertices are:

• $(5-3, 4) = (2,4)$
• $(5, 4-2) = (5,2)$
• $(5-3, 4-2) = (2,2)$

The coordinates of the other three vertices are $\boxed{(2,4), (5,2), \text{ and } (2,2)}$.

2. Whitney is drawing a square on a coordinate grid. The square has an area of 9 squares.

The area of a square is given by side length $\times$ side length.

The given vertex is $(6,9)$. Since the side length is 3 units, the other vertices can be found by adding or subtracting 3 from the x-coordinate and/or y-coordinate of $(6,9)$. There are four possible squares.

One possible set of coordinates for the other three vertices is:

• $(6-3, 9) = (3,9)$
• $(6, 9-3) = (6,6)$
• $(6-3, 9-3) = (3,6)$

Yes, there is more than one possible answer. For example, another set of vertices could be $(9,9)$, $(6,6)$, and $(9,6)$.

The coordinates of the other three vertices could be $\boxed{(3,9), (6,6), \text{ and } (3,6)}$.
Yes, there is more than one possible answer.

3. A rectangle has been drawn on a coordinate grid.

The image shows a rectangle with two given vertices: $(2,3)$ and $(5,7)$. These are opposite vertices of the rectangle.

For a rectangle aligned with the axes, if two opposite vertices are $(x_1, y_1)$ and $(x_2, y_2)$, then the other two vertices are $(x_1, y_2)$ and $(x_2, y_1)$.
Given $(2,3)$ and $(5,7)$:

• Vertex A has the x-coordinate of $(2,3)$ and the y-coordinate of $(5,7)$, so $\text{A} = (2,7)$.
• Vertex B has the x-coordinate of $(5,7)$ and the y-coordinate of $(2,3)$, so $\text{B} = (5,3)$.

The coordinates of vertices A and B are $\boxed{\text{A}=(2,7) \text{ and } \text{B}=(5,3)}$.

4. Work out the coordinates of points A, B and C.

The known coordinates are $(2,2)$, $(5,5)$, and $(8,8)$.

• Point A is the top-left corner of the upper rectangle.
• Point B is the bottom-right corner of the lower rectangle.
• Point C is the inner corner of the L-shape, specifically the bottom-left corner of the upper rectangle.

• For point A: Its x-coordinate aligns with the x-coordinate of $(5,5)$, which is 5. Its y-coordinate aligns with the y-coordinate of $(8,8)$, which is 8. So, $\text{A} = (5,8)$.
• For point B: Its x-coordinate aligns with the x-coordinate of $(8,8)$, which is 8. Its y-coordinate aligns with the y-coordinate of $(5,5)$, which is 5. So, $\text{B} = (8,5)$.
• For point C: Its x-coordinate aligns with the x-coordinate of $(2,2)$, which is 2. Its y-coordinate aligns with the y-coordinate of $(5,5)$, which is 5. So, $\text{C} = (2,5)$.

The coordinates of points A, B, and C are $\boxed{\text{A}=(5,8), \text{B}=(8,5), \text{ and } \text{C}=(2,5)}$.