Asksia AI LOGO

Sia

Question
Math
Posted 2 months ago

Quadrilateral ABCDA^{\prime} B^{\prime} C^{\prime} D^{\prime} is the result of dilating quadrilateral ABCDA B C D about point DD by a scale factor of 32\frac{3}{2}.

Determine whether each claim about the properties of ABCDA B C D and ABCDA^{\prime} B^{\prime} C^{\prime} D^{\prime} is true or false.

The perimeters of ABCDA B C D and ABCDA^{\prime} B^{\prime} C^{\prime} D^{\prime} are the same.
True/false

The lengths of CD\overline{C D} and CD\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)sqrt(17), 44, sqrt(61)sqrt(61), and 22
step 3
The perimeter of ABCD is sqrt(17)+4+sqrt(61)+2sqrt(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 32\frac{3}{2}. Thus, the perimeter of A'B'C'D' is 32(sqrt(17)+4+sqrt(61)+2)\frac{3}{2}(sqrt(17) + 4 + sqrt(61) + 2)
step 5
Simplifying the expression for the perimeter of A'B'C'D', we get 32×(sqrt(17)+4+sqrt(61)+2)sqrt(17)+4+sqrt(61)+2\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)sqrt(61)
step 7
The length of C'D' after dilation is 32×sqrt(61)\frac{3}{2} \times sqrt(61), which is not equal to sqrt(61)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