Click to select the figure in the image that would portray the rotation of the given preimage and the rotation arrow,
1 answer:
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Answer: The correct options are
(A) Rotation 90° anticlockwise.
(D) (x, y) → (–y, x).
Step-by-step explanation: Given that ΔXYZ is rotated to create the image triangle ΔX'Y'Z'.
Triangle XYZ and its image triangle X'Y'Z' are shown in the attached figure.
The co-ordinates of the vertices of ΔXYZ are X(0, 0), Y(0, -2) and Z(-2, -2).
And the co-ordinates of the vertices ΔX'Y'Z' are X'(0, 0), Y'(2, 0) and Z'(2, -2).
<u>Option (A) Rotation 90°:</u>
We see from the figure that if we rotate ΔXYZ is rotated 90° anticlockwise, then it will coincide with ΔX'Y'Z'.
So, rotation of 90° anticlockwise is a correct option.
<u>Option (B) Rotation 180°:</u>
If we rotate ΔXYZ is rotated clockwise or anticlockwise 180°, then it will NOT coincide with ΔX'Y'Z'.
So, rotation of 180° is NOT a correct option.
<u>Option (C) Rotation 270°:</u>
If we rotate ΔXYZ is rotated clockwise 270°, then also it will not coincide with ΔX'Y'Z'.
So, rotation of 270° clockwise is also a correct option.
<u>Option (D) (x, y) → (–y, x):</u>
We see that the co-ordinates of both the triangle follow the transformation
X(0, 0) ⇒ X'(0, 0)
Y(0, -2) ⇒ Y'(2, 0)
Z(-2, -2) ⇒ Z'(2, -2).
So, the transformation is (x, y) ⇒ (-y, x).
Therefore, the transformation (x, y) → (–y, x) is a correct option.
<u>Option (E) (x, y) → (y, -x):</u>
We see that the co-ordinates of both the triangle does NOT follow this transformation
For example, suppose this transformation is correct. Then, we have
Y(0, -2) ⇒ (-2, 0), which are not the co-ordinates of Y'.
Therefore, the transformation (x, y) → (–y, x) is NOT a correct option.
Thus, the correct options are:
(A) Rotation 90° anticlockwise.
(D) (x, y) → (–y, x).
Answer:
The length of the fence needed to surround this garden is 188 meters.
Step-by-step explanation:
Given : A fence is guarding off a vegetable garden in the form of a rectangle. It has one side that is 10 m greater than the other side.
To find : The length of the fence needed to surround this garden if the area of the vegetable garden is 2184 m² ?
Solution :
Let the one side of rectangle be 'x'.
Then the other side is 'x+10'.
The area of the rectangle is 2184 m²,
i.e.
Solve by middle term split,
Reject negative value,
The side of the rectangle is 42 m.
The other side is 42+10=52 m
The perimeter of the rectangle is
Therefore, the length of the fence needed to surround this garden is 188 meter.
Answer:
Step-by-step explanation:
Let be "x" the lenght in feet of rope that you can buy with 30 dollars.
According to the information provided in the exercise, you can buy a piece of rope of 2 feet with 20 cents.
Remember that
Knowing this, you can write the following proportion:
FInally, solving for "x", you get this result: