A light bulb is to be put in the middle of a room defined by the coordinates (10,5), (10,25), (20, 5) and (20,25). At what coordinate should the light bulb be placed?
Firstly we should try to establish the geometry of the room, ie identify the lines in which the walls lay.
Noticing that two of the points have the same x coordinate of x = 10 suggests that there must be a wall at x = 10. Similarly there must be a wall at x = 20 as this value is also shared by two points. To place the light bulb in the middle of the room, we must place it in the middle of two opposite walls, therefore the x coordinate must be in the middle of x = 10 and x = 20. This means that the x coordinate of the light bulb should be x = 15.
Now repeating the same process to identify the other two walls, we can see that there are two points with a y coordinate of y = 5 and two points with a y coordinate of y = 25. Therefore we can conclude that there must be walls at y = 5 and y = 25. This means that the y coordinate of the light bulb must also be in the middle of these two walls at y = 5 and y = 25, which is at y = 15.
Hence the coordinates of the light bulb must be (15,15)
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