Help please. 7th grade math. Need halo fast!
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<h2>Answer</h2>
After the dilation around the center of dilation (2, -2), our triangle will have coordinates:
First, we are going to translate the center of dilation to the origin. Since the center of dilation is (2, -2) we need to move two units to the left (-2) and two units up (2) to get to the origin. Therefore, our first partial rule will be:
→
Next, we are going to perform our dilation, so we are going to multiply our resulting point by the dilation factor . Therefore our second partial rule will be:
→
→
Now, the only thing left to create our actual rule is going back from the origin to the original center of dilation, so we need to move two units to the right (2) and two units down (-2)
→
→
Now that we have our rule, we just need to apply it to each point of our triangle to perform the required dilation:
Now we can finally draw our triangle:
<h3>Answer: Choice (b)</h3><h3>{ (1, 3), (3, 1), (4, 3) }</h3>
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Work Shown:
The notation "g o f" means g(f(x)). We have f(x) as the inner function that is computed first.
f(x) = { (1,2), (3,5), (4,1) }
The x coordinates of each point are: 1, 3, 4
The y coordinates are: 2, 5, 1
So the input x = 1 goes to y = 2 as the output. That output becomes the input of the g(x) function. Using x = 2 as the input for g, we see that 3 is the output. Check out the diagram below to see how each input goes into f, then goes into g to ultimately determine the x,y pairs. So far we've shown that x = 1 ultimately leads to y = 3.
Let's do another input: if x = 3 is plugged into f(x), then the output is 5 because of the point (3,5). Then x = 5 is plugged into g(x) to get x = 5 lead to y = 1. Ultimately x = 3 leads to y = 1 giving us (3,1) as another point.
Lastly, if x = 4 is plugged into f we get y = 1 as an output, which in turn is plugged into g to get 3 as the final output. The point (4,3) is the last ordered pair.
Again there's a lot to keep track of, so it helps to have a diagram as shown below.