Question

Math

Posted 2 months ago

```
Quadrilateral $A^{\prime} B^{\prime} C^{\prime} D^{\prime}$ is the result of dilating quadrilateral $A B C D$ about point $D$ by a scale factor of $\frac{3}{2}$.
Determine whether each claim about the properties of $A B C D$ and $A^{\prime} B^{\prime} C^{\prime} D^{\prime}$ is true or false.
The perimeters of $A B C D$ and $A^{\prime} B^{\prime} C^{\prime} D^{\prime}$ are the same.
True/false
The lengths of $\overline{C D}$ and $\overline{C^{\prime} D^{\prime}}$ are equal.
True/false
```

Sign in to unlock the answer

Answer from Sia

Posted 2 months ago

Solution by Steps

step 2

The perimeter of the original quadrilateral ABCD can be found by adding the distances between consecutive vertices. From the asksia-ll calculator, we have the distances as $sqrt(17)$, $4$, $sqrt(61)$, and $2$

step 3

The perimeter of ABCD is $sqrt(17) + 4 + sqrt(61) + 2$

step 4

To find the perimeter of the dilated quadrilateral A'B'C'D', we multiply each side of ABCD by the scale factor $\frac{3}{2}$. Thus, the perimeter of A'B'C'D' is $\frac{3}{2}(sqrt(17) + 4 + sqrt(61) + 2)$

step 5

Simplifying the expression for the perimeter of A'B'C'D', we get $\frac{3}{2} \times (sqrt(17) + 4 + sqrt(61) + 2) \neq sqrt(17) + 4 + sqrt(61) + 2$. Therefore, the perimeters of ABCD and A'B'C'D' are not the same

step 6

For the second statement, the length of CD is the distance between points C and D, which is $sqrt(61)$

step 7

The length of C'D' after dilation is $\frac{3}{2} \times sqrt(61)$, which is not equal to $sqrt(61)$. Therefore, the lengths of CD and C'D' are not equal

[question 1] Answer

False

[question 2] Answer

False

Key Concept

Dilation and Perimeter

Explanation

When a figure is dilated by a scale factor, the lengths of the sides are multiplied by that factor. This changes the perimeter proportionally to the scale factor.

Key Concept

Dilation and Side Lengths

Explanation

The length of a side after dilation is the original length multiplied by the scale factor. If the scale factor is not 1, the dilated length is different from the original length.

Not the question you are looking for? Ask here!

Enter question by text

Enter question by image

Upgrade to Asksia Pro

Join a AskSia's Pro Plan, and get 24/7 AI tutoring for your reviews, assignments, quizzes and exam preps.

Unlimited chat query usages

Strong algorithms that better know you

Early access to new release features

Study Other Question