Final answer:
The house's corners have the following coordinates: A = (-10,20), B = (-2,20), C = (-10,45), and D = (-2,45). If you live in house C, your position relative to house E is 8 units to the right. If house B is taken as the reference point, the positions of houses A, C, and D are A = (-8,25), C = (-8,25), and D = (0,25).
Step-by-step explanation:
The southeast corner of the plot is designated as the origin, which means its coordinates are (0,0). The other corners of the house are located at the points (-10,20), (-2,20), (-10,45), and (-2,45). Now, let's label these points: A = (-10,20), B = (-2,20), C = (-10,45), and D = (-2,45).
a. To draw a frame of reference with house A as the origin, we can draw a rectangular grid and plot the points A, B, C, and D accordingly. The positions of the houses are as follows:
- A = (-10,20)
- B = (-2,20)
- C = (-10,45)
- D = (-2,45)
b. If you live in house C, your position relative to house E can be found by subtracting the coordinates of C from the coordinates of E. Given that E = (-2,45) and C = (-10,45), the position of house E relative to house C is 8 units to the right.
c. To find the positions of houses A, B, and D, if house B is taken as the reference point, we can subtract the coordinates of B from the coordinates of A, C, and D. The positions are as follows:
- A = (-8,25)
- C = (-8,25)
- D = (0,25)