Use 3.14 for the value of pie , and round your answers to two decimal places, where applicable. If the radius of a circle is 3 c
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Please see the explanation of this question to see procedure for the dilation of the triangle ABC and the image attached below to know the result.
<h3>How to generated a resulting triangle by transformation rules</h3>
In this question we must apply a kind of <em>rigid</em> transformation known as dilation. A dilation of a point around a point of reference is defined by the following operation:
P'(x, y) = O(x, y) + k · [P(x, y) - O(x, y)] (1)
Where:
- O(x, y) - Point of reference
- k - Dilation factor
- P(x, y) - Original point
- P'(x, y) - Resulting point
Let assume that the point P is the origin of a <em>rectangular</em> system of coordinates. Then, the coordinates of the three vertices of the triangle ABC respect to the origin are: A(x, y) = (- 1, 2), B(x, y) = (- 1, - 1), C(x, y) = (2, 0).
Then, the vertices of the resulting triangle A'B'C' are, respectively:
A'(x, y) = (0, 0) + 3 · [(- 1, 2) - (0, 0)]
A'(x, y) = (- 3, 6)
B'(x, y) = (0, 0) + 3 · [(- 1, - 1) - (0, 0)]
B'(x, y) = (- 3, - 3)
C'(x, y) = (0, 0) + 3 · [(2, 0) - (0, 0)]
C'(x, y) = (6, 0)
Finally, we draw the resulting triangle with the help of a graphing tool.
To learn more on dilations: brainly.com/question/13176891
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The transformation of a function may involve any change. The transformation of the function is Right shift by 90 units.
<h3>How does the transformation of a function happen?</h3>The transformation of a function may involve any change.
Usually, these can be shifted horizontally (by transforming inputs) or vertically (by transforming output), stretched (multiplying outputs or inputs) etc.
If the original function is y = f(x), assuming the horizontal axis is the input axis and the vertical is for outputs, then:
Horizontal shift (also called phase shift):
Left shift by c units:
y=f(x+c) (same output, but c units earlier)
Right shift by c units:
y=f(x-c)(same output, but c units late)
Vertical shift:
Up by d units: y = f(x) + d
Down by d units: y = f(x) - d
Stretching:
Vertical stretch by a factor k:
Horizontal stretch by a factor k:
Since the function is transformed from f(x)=x to g(x)=x-90, therefore, the transformation of the function is Right shift by 90 units.
Learn more about Transforming functions:
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