Question

mya used the 10 ft side and the 8 ft side as corresponding sides. how could you use the numbers in the picture to get 1/3? remember, what mya is doing with the numbers is relevant. mya calculated the scale factor to be 1/2. what error, if any, could mya have made when she calculated the scale factor? mya only used the dimensions from the scale drawing of a rectangle. mya divided the dimensions, instead of multiplying them, to find the scale factor. mya did not make an error when she calculated the scale factor.

Explanation:

Step1: Recall Scale Factor Definition

Scale factor is \(\frac{\text{Scale Drawing Dimension}}{\text{Actual Dimension}}\) or \(\frac{\text{Actual Dimension}}{\text{Scale Drawing Dimension}}\)? Wait, no: Scale factor (for scaling down) is \(\frac{\text{Scale Drawing Length}}{\text{Actual Length}}\). Wait, let's check the rectangles. The actual rectangle (maybe the red one) has a side 10 ft? Wait, no, the blue one is 4 ft, red is 10 ft? Wait, no, the problem says "relation of a rectangle" – maybe the scale drawing is the blue one (4 ft) and actual is red (10 ft)? Wait, no, Mya calculated scale factor as \(\frac{1}{2}\). Let's see the options. Wait, the options are about her error. Let's analyze each option:

Option 1: "Mya only used the dimensions from the scale drawing of a rectangle." – No, scale factor needs both.

Option 2: "Mya used the 10 ft side and the 8 ft side as corresponding sides." – Wait, maybe the actual rectangle has sides 10 and 8? Wait, the blue one is 4 and... Wait, maybe the actual rectangle has length 10, scale drawing has 5? No, Mya got \(\frac{1}{2}\). Wait, maybe she divided the dimensions (like 4 and 8? No, the options: "Mya divided the dimensions, instead of multiplying them, to find the scale factor." Wait, no. Wait, the correct way: scale factor is \(\frac{\text{Scale Drawing}}{\text{Actual}}\). Suppose actual is 10, scale drawing is 5: \(\frac{5}{10}=\frac{1}{2}\). But if she used wrong corresponding sides. Wait, the option "Mya used the 10 ft side and the 8 ft side as corresponding sides" – no, maybe the actual rectangle has sides 10 and 8, and scale drawing has 4 and... Wait, no, the key is: when calculating scale factor, corresponding sides must be used. If she used 10 (actual) and 8 (actual) as corresponding to scale drawing sides, that's wrong. Wait, the correct error is: Wait, the options: "Mya divided the dimensions, instead of multiplying them, to find the scale factor." No, scale factor is division. Wait, no, let's re-express.

Wait, the correct answer is the option where she used non - corresponding sides. Wait, the option "Mya used the 10 ft side and the 8 ft side as corresponding sides" – no, maybe the actual rectangle has length 10 and width 8, and scale drawing has length 4 and width... Wait, no, Mya's error: if she took 4 (scale drawing) and 10 (actual) – \(\frac{4}{10}=\frac{2}{5}\), not \(\frac{1}{2}\). But she got \(\frac{1}{2}\). Wait, maybe she used 4 and 8? Wait, no, the options: "Mya divided the dimensions, instead of multiplying them, to find the scale factor." No, scale factor is division. Wait, the correct option is "Mya used the 10 ft side and the 8 ft side as corresponding sides" – no, wait, the last option: "Mya did not make an error when she calculated the scale factor." No, because if actual is 10 and 8, scale drawing is 4 and... Wait, maybe the actual rectangle has length 10, scale drawing has 5 (so \(\frac{5}{10}=\frac{1}{2}\)), but if she used 10 and 8 as corresponding, that's wrong. Wait, the correct answer is the option: "Mya used the 10 ft side and the 8 ft side as corresponding sides" – no, wait, the options:

Wait, the problem is about scale factor. The correct error is that she used non - corresponding sides. So the option "Mya used the 10 ft side and the 8 ft side as corresponding sides" – but wait, the options given:

Wait, the options are:

1. Mya only used the dimensions from the scale drawing of a rectangle.

2. Mya used the 10 ft side and the 8 ft side as corresponding sides.

3. Mya divided the dimensions, instead of multiplying them, to find the scale factor.

4. Mya did not make an error when she calculated the scale factor.

Wait, let's think again. Scale factor is \(\frac{\text{Scale Drawing Length}}{\text{Actual Length}}\). Suppose actual rectangle has length 10, width 8. Scale drawing has length 5, width 4. Then scale factor is \(\frac{5}{10}=\frac{1}{2}\) (or \(\frac{4}{8}=\frac{1}{2}\)). But if Mya used 10 (actual length) and 8 (actual width) as corresponding to scale drawing sides (like 4 and 5), that's wrong. So she used non - corresponding sides (10 and 8 as corresponding to scale drawing sides which are not their correspondents). So the error is "Mya used the 10 ft side and the 8 ft side as corresponding sides".

Answer:

The error Mya made is that she used non - corresponding sides. So the correct option is: Mya used the 10 ft side and the 8 ft side as corresponding sides. (Assuming the options are labeled, but from the text, the second option in the list: "Mya used the 10 ft side and the 8 ft side as corresponding sides".)