Question

find the composition of transformations that map abcd to ehgf. reflect over the x - axis, then translate (x + 3,y+?).

Explanation:

Step1: Find the coordinates of point \( B \)

The coordinates of point \( B \) are \( (-3,4) \).

Step2: Reflect point \( B \) over the \( x - axis \)

When reflecting a point \( (x,y) \) over the \( x - axis \), the transformation is \( (x,-y) \). So, reflecting \( B(-3,4) \) over the \( x - axis \) gives \( (-3,-4) \).

Step3: Assume the translation rule is \( (x + 3,y + k) \) and find the coordinates of the corresponding point \( H \)

Let's assume the corresponding point of \( B \) after transformation is \( H \). The coordinates of \( H \) are \( (0,-3) \).
Using the translation formula:
If \( x=-3 \), after \( x+3 \) transformation, \( x'=-3 + 3=0 \)
If \( y=-4 \), after \( y + k \) transformation, \( y'=-4 + k \)
Since \( y'=-3 \), we have the equation \( -4 + k=-3 \)

Step4: Solve the equation for \( k \)

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Answer:

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