Consider that ΔXYZ is reflected across the y-axis and translated 2 units down.
Choose all TRUE statements about the transformation.
1) X'Y' ≅ XY
2) ∠Z ≅ ∠Z'
3)ΔXYZ is not congruent to ΔX'Y'Z'.
4)Reflecting and translating the triangle change its shape and size.
I've been trying to figure out the answer to this for a while and can't, please help.
wrong
its 1 and 2
Think about the difference between "similar" and "congruent"...
Once you have narrowed it down, we would be happy to check your answers : )
i was thinking one and three
Do you think the angles change when you slide, and flip the triangle?
No...
So then isn't #2 correct as well?
so is it 1, 2, & 3??
Correct : )
thank you so much
To determine the true statements about the given transformation, let's break it down step by step.
1) Reflecting ΔXYZ across the y-axis:
When reflecting a figure across the y-axis, the x-coordinates remain the same, but the signs of the y-coordinates change. So, for each point (x, y) in ΔXYZ, the corresponding point (x', y') in the reflected image ΔX'Y'Z' will have the same x-coordinate but the opposite sign for the y-coordinate.
2) Translating ΔX'Y'Z' 2 units down:
When translating a figure, all the points are moved in the given direction by the specified amount. In this case, translating ΔX'Y'Z' 2 units down means shifting all the points vertically downward by 2 units.
Now let's evaluate the statements:
1) X'Y' ≅ XY:
Since reflecting the triangle only changes the sign of the y-coordinates, and translating does not affect the length of the sides, the statement is true. X'Y' will be congruent to XY.
2) ∠Z ≅ ∠Z':
When reflecting a figure across the y-axis, the angles remain the same. Translating the triangle vertically downward by 2 units also does not affect the angle measures. Therefore, the statement is true. ∠Z is congruent to ∠Z'.
3) ΔXYZ is not congruent to ΔX'Y'Z':
This statement is false. Reflecting and translating a figure do not change the size or shape of congruent figures. Therefore, ΔXYZ will still be congruent to ΔX'Y'Z'.
4) Reflecting and translating the triangle change its shape and size:
This statement is false. Reflecting a figure across the y-axis does not change its shape or size, but only its orientation. Translating the figure only moves the shape in space without altering its size or shape.
So, the true statements are:
1) X'Y' ≅ XY
2) ∠Z ≅ ∠Z'