Question

Rectangles P, Q, R, and S are scaled copies of one another. For each pair, decide if the scale factor from one to the other is greater than 1, equal to 1, or less than 1. Four rectangles, labeled P, Q, R and S. Each rectangle is a scaled copy of one another. Ranked in order from least to greatest, the area of the rectangles are as follows: the area of P is equal to S, which are less than the area of Q, which is less than the area of R. From P to Q from P to R from Q to S from Q to R from S to P from R to P from P to S

Answer 1

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Answer:

In summary, the true statements are:

- The scale factor from R to S is greater than 1.

- The scale factor from P to Q is greater than 1.

- The scale factor from S to R is greater than 1.

- The scale factor from S to P is exactly 1.

Explanation:

Rectangles P, Q, R, and S are scaled copies of one another. To determine which statements are true, let's consider the properties of scaled copies.

1. The scale factor from R to S is greater than 1.

This statement is true. When going from R to S, the scale factor is greater than 1 because S is larger than R.

2. The scale factor from P to Q is greater than 1.

This statement is true. When going from P to Q, the scale factor is greater than 1 because Q is larger than P.

3. The scale factor from P to S is less than 1.

This statement is false. Since P and S are scaled copies of each other, the scale factor from P to S is equal to 1. They have the same size.

4. The scale factor from R to Q is less than 1.

This statement is false. Since R and Q are scaled copies of each other, the scale factor from R to Q is equal to 1. They have the same size.

5. The scale factor from S to R is greater than 1.

This statement is true. When going from S to R, the scale factor is greater than 1 because R is smaller than S.

6. The scale factor from P to R is less than 1.

This statement is false. Since P and R are scaled copies of each other, the scale factor from P to R is equal to 1. They have the same size.

7. The scale factor from S to P is exactly 1.

This statement is true. Since P and S are scaled copies of each other, the scale factor from S to P is equal to 1. They have the same size.

In summary, the true statements are:

- The scale factor from R to S is greater than 1.

- The scale factor from P to Q is greater than 1.

- The scale factor from S to R is greater than 1.

- The scale factor from S to P is exactly 1.

Answer 2

I attached a diagram that will aid the understanding of the question.

Firstly, I would love to review what a scale factor is before going into the question.

If you have two shapes that are similar, that is they have corresponding angles, then the scale factor of one to the other is simply the ratio of any two corresponding lengths in the two similar geometric figures.

Looking at these figures in the question, we see that R is an enlargement of the other rectangles while Q is an enlargement of P and S. With this information we can answer the questions:

1. From P to Q, the scale factor greater than one because Q is bigger than P.

2. From P to R, the scale factor is greater than one for the same reason.

3. From Q to S, the scale factor is less than one because S is smaller than Q.

4. From Q to R, the scale factor is greater than one because R is bigger than Q.

5. From S to P, the scale factor is equal to one because they are equal.

6. From R to P, the scale factor is less than one because p is smaller than R.

7. From P to S, the scale factor is equal to one because they are equal.