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Whitepunk [10]
3 years ago
8

Triangle △ABC is in the first quadrant and translated along ‹ 3, 7 › and reflected across the x-axis. Which quadrant will the tr

iangle be in after the first transformation? Which quadrant will the triangle be in after the second transformation?
Mathematics
1 answer:
wel3 years ago
5 0

Answer:

The triangle will be in the first quadrant after the 1st transformation

The triangle will be in the fourth quadrant after the 2nd transformation

Step-by-step explanation:

* <em>Lets revise translation and reflection</em>

- Horizontal translation means move the figure to right or to left

- Vertical translation means move the figure up or down

- Reflection across x-axis reverses the figure from up the x-axis to

 down the x-axis or reverses it from down the x-axis to up the x-axis

* <em>Lets solve the problem</em>

- Triangle △ABC is in the first quadrant

- It translated along ‹ 3, 7 ›

- Then reflected across the x-axis

- We need to know the image of the triangle after first transformation

 lies in which quadrant and after the second transformation lies in

 which quadrant

∵ The triangle in first quadrant

∵ The translation is <3 , 7>

- That means the triangle is translated 3 units to the right and

  7 units up

∴ The triangle still in the first quadrant

* The triangle will be in the first quadrant after the 1st transformation

∵ The triangle reflected across the x-axis

- That means the triangle is reversed from up the x-axis to down

 the x-axis

∴ The triangle is reversed to the fourth quadrant

* The triangle will be in the fourth quadrant after the 2nd transformation

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Using a system of equations, it is found that since 20 child bikes and 6 adult bikes would require more testing than the allocated time, it is not possible to build this amount.

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A system of equations is when two or more variables are related, and equations are built to find the values of each variable.

In this problem, the variables are:

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Each child bike requires 4 hours to build, as do each adult bike. The company has 100 hours of testing, hence:

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With 20 child bikes and 6 adult bikes in a week, we have that c = 20, a = 26, hence:

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Writing an equation the statement, we obtain

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