Karisha drew pentagon A on a coordinate grid. She then performed a rotation followed by a dilation with scale factor 5 to produc
e pentagon B. Which is a true statement about the two pentagons? A. They are similar, but not congruent. B. They are neither congruent nor similar. C. They are similar and congruent. D. They are congruent, but not similar.
1 answer:
Answer:
A.
Step-by-step explanation:
Rotation is a transformation that turns a figure about a fixed point. An object and its rotation image are the same shape and size, but the figures may be turned in different directions. So, rotation gives us two congruent pentagons.
Dilation is a transformation that produces an image that is the same shape as the original (similar to original), but is a different size. So, dilation gives us two similar pentagons.
A sequence of rotation and dilation produces pentagon that is similar to the initial, but not congruent.
In attached diagram you can see the pictorial representation:
- pentagon FGHIJ is the rotation image of pentagon ABCDE
- pentagon KLMNO is dilation image of pentagon FGHIJ
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Answer:
Γ = 15
Step-by-step explanation:
Given
f(x) = x² - 8x + Γ
with a = 1, b = - 8 and c = Γ , then
sum of zeros α + β = - = -
= 8
product of zeros = αβ = = Γ
Given α - β = 2 , then
(α - β)² = 2²
α² - 2αβ + β² = 4 → (1)
and
(α + β)² = 8²
α² + 2αβ + β² = 64 → (2)
Add (1) and (2) term by term
2α² + 2β² = 68 ( divide through by 2 )
α² +β² = 34
Substitute α² + β² = 34 into (1)
34 - 2αβ = 4 ( subtract 34 from both sides )
- 2αβ = - 30 ( divide both sides by - 2 )
αβ = 15
Now
αβ = Γ = 15
Thus
f(x) = x² - 8x + 15