Question

Use the image to answer the question.

A coordinate plane shows two triangles A B C and A double dash B double dash C double dash. Both the axes range from negative 6 to 6 in unit increments.

Identify the sequence of transformations that will carry ΔABC→ΔA"B"C"
. Give your answer in the form of a composition transformation mapping.

(1 point)
Responses

(x,y)→(x−4,−y)
left parenthesis x comma y right parenthesis right arrow left parenthesis x minus 4 comma negative y right parenthesis

(x,y)→(x+4,−y)
left parenthesis x comma y right parenthesis right arrow left parenthesis x plus 4 comma negative y right parenthesis

(x,y)→(x,−y+4)
left parenthesis x comma y right parenthesis right arrow left parenthesis x comma negative y plus 4 right parenthesis

(x,y)→(x,−y−4)

Answer 1

I can’t see the image you mentioned. Could you re-upload it or list the coordinates of A, B, C and A″, B″, C″?

If you want to check yourself, use this quick method:
- Compare a corresponding vertex, e.g. A(x,y) → A″(x″,y″).
- If y″ = −y (or y″ = −y + k) that indicates a reflection in the x-axis possibly followed by a vertical shift; if x changes sign it indicates reflection in the y-axis.
- Then find the translation vector: (x″ − x, y″ − (−y)) if you first reflect across the x-axis.

For example:
- If A″ = (x+4, −y) for every vertex then the rule is (x,y) → (x+4, −y).
- If A″ = (x−4, −y) then the rule is (x,y) → (x−4, −y).
- If A″ = (x, −y+4) then the rule is (x,y) → (x, −y+4), etc.

Send the image or coordinates and I’ll pick the correct option.