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?

Here are the solutions to the problems: 1. A rectangle has been drawn on a coordinate grid. Step 1: Identify the given vertex and observe the rectangle's dimensions from the grid. 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. Step 2: Use the dimensions to find the other vertices. 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 (2,4), (5,2), and (2,2). 2. Whitney is drawing a square on a coordinate grid. The square has an area of 9 squares. Step 1: Calculate the side length of the square. The area of a square is given by side length × side length. Side length = sqrt(Area) = sqrt(9) = 3 units Step 2: Determine the possible coordinates for the other three vertices. 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 (3,9), (6,6), and (3,6). Yes, there is more than one possible answer. 3. A rectangle has been drawn on a coordinate grid. Step 1: Identify the given vertices and their relationship. The image shows a rectangle with two given vertices: (2,3) and (5,7). These are opposite vertices of the rectangle. Step 2: Determine the coordinates of vertices A and B. 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 A = (2,7). Vertex B has the x-coordinate of (5,7) and the y-coordinate of (2,3), so B = (5,3). The coordinates of vertices A and B are A=(2,7) and B=(5,3)*. 4. Work out the coordinates of points A, B and C. Step 1: Identify the known coordinates and the positions of A, B, and C on the L-shaped figure. 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. Step 2: Determine the coordinates for A, B, and C by observing their alignment with the grid lines and known points. 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, 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, 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, C = (2,5). The coordinates of points A, B, and C are A=(5,8), B=(8,5), and C=(2,5)*. Send me the next one 📸