Question

1. graph & label the images of the sequence of transformations.

translate parallelogram math \\((x,y) \
ightarrow (x, y+6)\\)
reflect parallelogram math over the y-axis

Explanation:

Identify original coordinates

Identify the coordinates of the vertices of parallelogram \(MATH\) from the grid:

• \(M(-5, -2)\)
• \(A(-1, -2)\)
• \(T(-3, -5)\)
• \(H(-7, -5)\)

Apply translation

Apply the translation rule \((x, y)
ightarrow (x, y+6)\) to find the coordinates of \(M'A'T'H'\):

• \(M'(-5, -2+6) = M'(-5, 4)\)
• \(A'(-1, -2+6) = A'(-1, 4)\)
• \(T'(-3, -5+6) = T'(-3, 1)\)
• \(H'(-7, -5+6) = H'(-7, 1)\)

Apply reflection

Reflect the translated parallelogram \(M'A'T'H'\) over the \(y\)-axis using the rule \((x, y)
ightarrow (-x, y)\) to find \(M''A''T''H''\):

• \(M''(5, 4)\)
• \(A''(1, 4)\)
• \(T''(3, 1)\)
• \(H''(7, 1)\)

Answer:

The coordinates of the vertices after each transformation are:

Original Parallelogram \(MATH\):

• \(M(-5, -2)\)
• \(A(-1, -2)\)
• \(T(-3, -5)\)
• \(H(-7, -5)\)

**After Translation \((x, y)
ightarrow (x, y+6)\) to form \(M'A'T'H'\):**

• \(M'(-5, 4)\)
• \(A'(-1, 4)\)
• \(T'(-3, 1)\)
• \(H'(-7, 1)\)

After Reflection over the \(y\)-axis to form \(M''A''T''H''\):

• \(M''(5, 4)\)
• \(A''(1, 4)\)
• \(T''(3, 1)\)
• \(H''(7, 1)\)