Question

graph the image of trapezoid tuvw after a translation 2 units left and a reflection over the y-axis.

Explanation:

Identify original coordinates

Find the coordinates of the vertices of trapezoid \(TUVW\) from the given graph:

• \(T = (3, 4)\)
• \(U = (4, 4)\)
• \(V = (5, 1)\)
• \(W = (2, 1)\)

Apply translation

Using the Translation knowledge point, shift each vertex 2 units left:

$$(x, y) \to (x - 2, y)$$

• \(T' = (3 - 2, 4) = (1, 4)\)
• \(U' = (4 - 2, 4) = (2, 4)\)
• \(V' = (5 - 2, 1) = (3, 1)\)
• \(W' = (2 - 2, 1) = (0, 1)\)

Apply reflection

Using the Reflection knowledge point, reflect each translated vertex over the \(y\)-axis:

$$(x, y) \to (-x, y)$$

• \(T'' = (-1, 4)\)
• \(U'' = (-2, 4)\)
• \(V'' = (-3, 1)\)
• \(W'' = (0, 1)\)

Verify final coordinates

The final coordinates of the transformed trapezoid \(T''U''V''W''\) are:

• \(T'' = (-1, 4)\)
• \(U'' = (-2, 4)\)
• \(V'' = (-3, 1)\)
• \(W'' = (0, 1)\)

Answer:

The coordinates of the image of trapezoid \(TUVW\) after a translation 2 units left and a reflection over the \(y\)-axis are:

• \(T'' = (-1, 4)\)
• \(U'' = (-2, 4)\)
• \(V'' = (-3, 1)\)
• \(W'' = (0, 1)\)