Question

Which of these triangle pairs can be mapped to each other using two reflections? Triangles X Y Z and P Y T are connected at point Y. Triangle X Y Z is reflected across X Y and then is reflected another time across Y Z to form triangle P Y T. Triangles X Y Z and A Y T are connected at point Y. Triangle X Y Z is reflected 3 times to form triangle A Y T. Triangles X Y Z and A Y T are connected at point Y. Triangle X Y Z is reflected across side X Y and then is shifted down to form triangle A Y T. Triangles X Y Z and A Z T are connected at point Z. Triangle X Y Z is reflected and then rotated to form triangle A Z T.

Answer 1

Answer:

The correct option is the first option;

Triangle XYZ and PYT are connected at point Y. Triangle XYZ is reflected across XY and then is reflected another time across YZ to form triangle PYT

Step-by-step explanation:

To answer the question we look at each option as follows;

1) The parameters given are triangle XYZ and PYT are connected at point Y

Triangle XY is reflected about XY will shift the marked angle from left to right while the right angle will remain at the same location and the triangle will remain upright to give triangle X'Y'Z'

Reflection about the YZ will give; the marked angle and the right angle in the same location and the vertex X will then be changed to P

Therefore, triangle XYZ can be mapped to triangle PYT with two reflections

2)  In the second option, we have triangle XYZ is reflected 3 times which is more than 2 times as in the question, therefore, option two is less suited as an answer to the question

3) Triangle XYZ is reflected across side XY and then is shifted down to form triangle AYT

Therefore, since we have only one reflection, option 3 is also not appropriate as an answer

4) In option 4 triangle XYZ is reflected and then rotated therefore option 4 is also not a correct option.

Answer 2

The correct option is  (A). $\Delta XYZ$ and $\Delta PYT$ are connected at point Y. $\Delta XYZ$ is reflected across XY and then is reflected another time across YZ to form $\Delta PYT$.

Given, $\Delta XYZ$ and $\Delta PYT$ are connected at point Y.

$\Delta XYZ$ is reflected about XY will shift the marked angle from left to right while the right side angle will remain at the same location and the triangle will remain upright to give$\Delta X'Y'Z'.$

Reflection about the YZ will give the marked angle and the right angle in the same location and the vertex X will then be changed to P.

Thus , $\Delta XYZ$ can be mapped to $\Delta PYT$ with two reflections.

In the second option, we have $\Delta XYZ$ is reflected 3 times which is more than 2 times as said in question. so this statement is false.

In next option $\Delta XYZ$ is reflected across side XY and then is shifted downwards to form $\Delta AYT$ . since here we have only one reflection, so this statement is also false.

4) In option 4 $\Delta XYZ$ is reflected and then rotated thus option 4 is also not a correct option.

Hence the correct statement is $\Delta XYZ$ and $\Delta PYT$ are connected at point Y. $\Delta XYZ$ is reflected across XY and then is reflected another time across YZ to form $\Delta PYT$.

For more detail follow the link:

https://brainly.com/question/8668014