Which of these triangle pairs can be mapped to each other using both a translation and a reflection across the line containing AB? Triangles X Y Z and A B C are congruent. Triangle X Y Z is reflected across a line to form triangle A B C. It is also slightly higher than triangle A B C. Triangles A B C and A Y C are congruent and share common side A C. Triangle A B C is reflected across line A C to form triangle A Y C. Triangles A B C and X Y Z are congruent. Triangle X Y Z is slightly higher and to the right of triangle A B C. Triangles A B C and X Y Z are congruent. Triangle A B C is rotated to the right to form triangles X Y Z. Triangle X Y Z is also higher and to the right of triangle A B C.

B. Triangles A B C and A Y C are congruent and share common side A C. Triangle A B C is reflected across line A C to form triangle A Y C.

Step-by-step explanation:

Translation and reflection are examples of methods of rigid transformation. Translation ensure that each point on a given figure is moved the same distance with respect to the reference plane. Reflection involves the flipping of a given figure across a given line.

From the question, both reflection and transformation would map the triangles into one another. Since the reference line contains AB, then the two triangles are congruent and would share a common side.

Thus, the triangle pairs that can be mapped into each other is that of option B.

Based on the information given, the triangle pairs that can be mapped to each other using both a translation and a reflection across the line containing AB will be A. Triangles X Y Z and A B C are congruent. Triangle X Y Z is reflected across a line to form triangle A.

Triangles.

The triangle pair that can be mapped to each other using both translation and reflection across line containing AB is the first triangle pair.

The first figure consists of ΔXYZ and ΔABC that are a reflection of each other across the line AB and a translation.

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2.4080 meters.

Remember that the definition of work is force over distance. And that the gravitational potential energy that the turtle has will exactly match the work performed in lifting it. So have the following variables
Mass = 860.24 kg
Work = 20320.7 J = 20320.7 kg*m^2/s^2
Gravitational acceleration = 9.81 m/s^2
And we wish to get an answer in meters. So we need to multiply and divide the three numbers we have with all their related units and derive an answer with the unit of m. We can cancel out most of the units by dividing the work by the gravitational acceleration, so
20320.7 kg*m^2/s^2 / 9.81 m/s^2 =  2071.427 kg*m

Now we can cancel out the kg unit by dividing by the mass of the turtle. So
2071.427 kg*m / 860.24 kg =  2.407964 m

Rounding to 5 significant figures gives 2.4080 meters.