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Answer: Ro, 270° and Ro -90°
Step-by-step explanation: If the vertex is at 5 on the y-axis at (0,5) and the transformation has moved the vertex to (5,0) it is now at +5 on the x-axis. This is a rotation around the origin, Rotation notation Ro.
This is fairly easy to visualize: like the hand of an analog clock moving from 12 o'clock to 3 o'clock.
In geometry, rotations are given in degrees, moving <u>counter-clockwise.</u> There are 360° in a circle.
Moving 3/4 of the way around the circle counterclockwise.
Multiply(3/4)(360) = 270. This is a positive rotation, counter-clockwise
Clockwise, it is 1/4 of the circle, so Multiply (1/4)(360)= 90 But remember to <u>add the negative sign because </u><em><u>clockwise is considered a negative rotation.</u></em>
<u>Ro, -90°</u>
The two transformations are reflection across the x-axis and translation 8 units down
Step-by-step explanation:
Let us revise some transformations
- If the function f(x) reflected across the x-axis, then its image is g(x) = - f(x)
- If the function f(x) reflected across the y-axis, then its image is g(x) = f(-x)
- If the function f(x) translated vertically up by k units, then its image is g(x) = f(x) + k
- If the function f(x) translated vertically down by k units, then its image is g(x) = f(x) - k
∵ f(x) =
∵ f(x) is transformed into the function g(x)
∵ g(x) = - 8
- The negative sign in front of means f(x) becomes
-f(x), so f(x) is reflected across the x-axis as the 1st rule above
∴ f(x) is reflected across the x-axis
- Then 8 is subtracted from , that means -f(x)
becomes -f(x) - 8, so -f(x) is translated 8 units down as the 4th
rule above
∴ f(x) then translated 8 units down
The two transformations are reflection across the x-axis and translation 8 units down
The graph of g(x) is the image of the graph of f(x) by reflection across the x-axis and then translation 8 units down
Look for the attached graph which represents f(x) and g(x)
The red graph is reflected across the x-axis the part of the graph over the x-axis becomes under the x-axis and the part of the graph under the x-axis becomes over the x-axis and then the graph translated 8 units down represented by the blue graph
Learn more:
You can learn more about transformation in brainly.com/question/5563823
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