Which of these properties of a rigid transformation is exclusive to translations?
2 answers:
Answer with explanation:
There are four kind of Rigid transformation that can take place in a two dimensional or Three dimensional geometrical Shape
1. Rotation
2. Reflection
3.Dilation
4. Translation
When we translate a geometrical shape , the Preimage , shifts from one position to another position in the plane in which it lies ,without changing the shape ,size ,and Interior angle of the PreImage.
→→I have described first three properties ,which are true to translation by taking a triangle ,having vertices , (0,0), (0,1) and (1,0).
Now, translating the triangle , by 1 unit right and 1 unit up,got the triangle having vertices, (1,1),(1,2) and (2,1).
Option 4 : The orientation of sequences of points in the pre image are always preserved, is the property of a rigid transformation that appears exclusive to translations.
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The steps to prove the given statement by using the properties of multiplication.
Solution:
We have,
Taking left hand side, we get
(Associative property of multiplication)
Hence proved.
Answer:
The value of k = 4/3
Step-by-step explanation:
* Lets explain how to solve the problem
- An equilateral triangle ABC is inscribed in a circle N
- The area of the triangle is √3
- The shaded area is the difference between the area of the circle
and the area of the equilateral triangle ABC
- The shaded are = k π - √3
- We need to find the value of k
* <u><em>At first lets find the length of the side of the Δ ABC</em></u>
∵ Δ ABC is an equilateral triangle
∴ Its area = √3/4 s² , where s is the length of its sides
∵ The area of the triangle = √3
∴ √3/4 s² = √3
- divide both sides by √3
∴ 1/4 s² = 1
- Multiply both sides by 4
∴ s² = 4 ⇒ take √ for both sides
∴ s = 2
∴ The length of the side of the equilateral triangle is 2
* <u><em>Now lets find the radius of the circle</em></u>
- In the triangle whose vertices are A , B and N the center of the circle
∵ AN and BN are radii
∴ AN = BN = r , where r is the radius of the circle
∵ The sides of the equilateral angles divides the circle into 3 equal
arcs in measure where each arc has measure 360°/3 = 120°
∵ The measure of the central angle in a circle equal the measure
of the its subtended arc arc
∵ ∠ANB is an central angle subtended by arc AB
∵ The measure of arc AB is 120°
∴ m∠ANB = 120°
- By using the cosine rule in Δ ANB
∵ AB = 2 , AN = BN = r , m∠ANB = 120°
∴
∴
∴
∴
∴
- Divide both sides by 3
∴
- Take square root for both sides
∴ r = 2/√3
* <u><em>Lets find the value of k</em></u>
∵ Area circle = πr²
∵ r = 2/√3
∴ Area circle = π(2/√3)² = (4/3)π
∵ Area shaded = area circle - area triangle
∵ Area triangle = √3
∴ Area shaded = (4/3) π - √3
∵ Area of the shaded part is π k - √3
- Equate the two expressions
∴ π k - √3 = (4/3) π - √3
∴ k = 4/3
* The value of k = 4/3