Question

Identify the glide reflection rule to map ΔABC onto ΔA′B′C′ in the given figure.Question 19 options:A) Translation: (x, y) → (x, y – 4); Reflection across the y-axisB) Translation: (x, y) → (x, y – 4); Reflection across the x-axisC) Translation: (x, y) → (x, y + 4); Reflection across the x-axisD) Translation: (x, y) → (x + 4, y); Reflection across the x-axis

Answer 1

`\begin{gathered} Translation\colon(x,y)\text{ }\to(x,y-4); \\ Reflection\text{ across the y-ax is (option A)} \end{gathered}`

Step-by-step explanation:

Let's state the coordinates of triangle ABC and A'B'C':

A = (-3, 5), A' = (3, 1)

B = (-7, 4), B' = (7, 0)

C = (-5, 1), C' = (5, -3)

A reflection over the y - axis:

`\begin{gathered} (x,\text{ y) }\rightarrow\text{ (-x, y)} \\ A\colon\text{ from -3 to 3} \\ B\colon\text{ from -7 to 7} \\ C\colon\text{ from -5 to 5} \end{gathered}`

Then a translation of 4 units to the left:

`\begin{gathered} \text{The y coordinate of the original is reduced by 4} \\ (x,\text{ y) }\rightarrow\text{ (}x,\text{ y - 4)} \\ A\colon\text{ from 5 to 1} \\ B\colon\text{ from 4 to 0} \\ C\colon\text{ from 1 to -3} \end{gathered}`
`\begin{gathered} Translation\colon(x,y)\text{ }\to(x,y-4); \\ Reflection\text{ across the y-ax is (option A)} \end{gathered}`