A scale drawing of the floor of a theater has a scale factor of 18. Mark says that he can use this information and any length on the scale drawing to find the corresponding length and the actual theater. He says that he can also use this information and any length in the actual theater to find the corresponding length on the scale drawing. Is Mark correct? I really don't understand. I would really appreciate help.
Thank you!
Do you know what a scale factor is?
e.g. there are 12 inches in a foot
so if we have a patio which is 10 ft by 14 ft, I could make a drawing where 1 inch repesents 1 foot. My scale factor is 12
so I would draw my patio as 10 inches by 14 inches
In our case the scale factor is 18
so 1 unit on the paper sketch would be 18 units in reality.
so if Mark sketched a room as 8 inches by 10 inches, then the actual dimensions of the room would be
8(18)inches by 10(18) inches
= 144 inches by 180 inches
= 12 ft by 15 ft
to go from the real world down to a sketch, we would divide the dimensions by the scale factor
Yes, Mark is correct. The scale factor of 18 means that every length on the scale drawing is 18 times smaller than the corresponding length in the actual theater.
To find the corresponding length in the actual theater using a length on the scale drawing, you simply multiply the length on the scale drawing by the scale factor. For example, if a length on the scale drawing is 5 units, then the corresponding length in the actual theater would be 5 * 18 = 90 units.
To find the corresponding length on the scale drawing using a length in the actual theater, you would divide the length in the actual theater by the scale factor. So if a length in the actual theater is 100 units, then the corresponding length on the scale drawing would be 100 / 18 = 5.56 units (rounded to the nearest hundredth).
In both cases, you can use the scale factor and any length to find the corresponding length in the other context.
Yes, Mark is correct. The scale factor of 18 means that every unit on the scale drawing represents 18 units in the actual theater. This allows you to easily find the corresponding lengths between the scale drawing and the actual theater.
To find the corresponding length in the actual theater when you have a length on the scale drawing, you simply need to multiply that length by the scale factor. For example, if you have a length of 5 units on the scale drawing, the corresponding length in the actual theater would be 5 units * 18 = 90 units.
Similarly, to find the corresponding length on the scale drawing when you have a length in the actual theater, you need to divide that length by the scale factor. For example, if a length in the actual theater is 180 units, the corresponding length on the scale drawing would be 180 units / 18 = 10 units.
In summary, the scale factor allows you to easily convert between lengths on the scale drawing and lengths in the actual theater.