Question

Triangle △ABC is in the first quadrant and translated along ‹ 3, 7 › and reflected across the x-axis. Which quadrant will the triangle be in after the first transformation? Which quadrant will the triangle be in after the second transformation?

Answer 1

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:

* Lets revise translation and reflection

- 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

* Lets solve the problem

- 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