Translate triangle a by vector (-3/1)to give triangle b. Then rotate your triangle b 180 degrees around the origin to give trian
gle. Describe fully the single transformation that maps triangle a onto triangle c
1 answer:
Answer:
Rotate triangle A about the point (1.5, -0.5) by 180°.
Step-by-step explanation:
Translating a figure by a vector means shifting it 3 units left along the x-axis and 1 unit up along the y-axis.
The translation rule can be expressed as:
(x, y) → [(x - 3), (y + 1)]
Based on the provided figure,
The coordinates of triangle A are A(1, -1), B(1, -4) and C(3, -4)
Post-translation, the new coordinates are A'(-2, 0), B'(-2, -3), C'(0, -3).
Next, applying a 180° rotation to these new points about the origin gives:
Rotation rule:
(x, y) → (-x, -y)
A'(-2, 0) → A"(2, 0)
B'(-2, -3) → B"(2, 3)
C'(0, -3) → C"(0, 3)
Thus, the transformation A(1, -1) → A"(2, 0) represents the entire transformation.
The rule defining the transformation mapping triangle C to A would be expressed as:
Rotate triangle A about the point (1.5, -0.5) by 180°.
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Answer:
The rotation angle measures 2.11 °
Step-by-step explanation:
Stated as follows:
The radius of the circular path = r = 18 feet
The distance rolled by the wheel = l = 38 feet
Let us denote the angle of rotation as Ф
Now, according to the problem:
∵ the length of an arc at the center corresponds to an angle Ф
Thus,
distance rolled by the wheel = π × radius ×
As 180° represents π radians
And π approximates to 3.14
Thus, distance rolled by the wheel = 180 °× radius ×
That is l = r × Ф
So, Ф =
Consequently, Ф =
Therefore, Ф = 2.11 °
Thus, the rotation angle is Ф = 2.11 °
Hence, the rotation angle is 2.11 ° Answer