Rectangle PQRS is reflected across the x-axis. The image is P′Q′R′S′. Which two further transformations will carry rectangle P′Q′R′S′ back onto rectangle PQRS?
idk
To find the two further transformations that will carry rectangle P'Q'R'S' back onto rectangle PQRS, we need to analyze the effects of the reflection across the x-axis and understand how it changes the shape of the original rectangle.
1. Reflection across the x-axis: This transformation involves taking each point of the original rectangle PQRS and reflecting it across the x-axis to obtain the image P'Q'R'S'. For example, point P(x, y) on the original rectangle will become P'(x, -y) in the reflected image.
To carry P'Q'R'S' back onto PQRS, we need to perform two additional transformations:
2. Reflection across the y-axis: This transformation involves taking each point of the reflected rectangle P'Q'R'S' and reflecting it across the y-axis to obtain a new shape. This reflection will cancel out the initial reflection across the x-axis and restore the original shape of the rectangle. For example, point P'(x, -y) will become P''(-x, -y) after the reflection across the y-axis.
3. Translation: After reflecting the shape across the y-axis, it is usually necessary to perform a translation to move the second shape back to its original position. A translation involves moving each point of the shape along a specified distance and direction. In this case, we need to shift the entire shape by the same amount in the positive x-direction so that P'' is aligned with P.
By applying the reflection across the y-axis and then translating the shape to the right, we can carry the reflected rectangle P'Q'R'S' back onto the original rectangle PQRS.
Remember, the order in which transformations are applied matters. In this case, we perform the reflection across the y-axis first and then the translation.