Question

7. Quadrilateral
STUV with vertices S(-3, -3),
T(3, -5), U(6, -7), and V(-2, -7): y = -4

Answer 1

Explanation:

S=-3,3 T=3,-5 U=6,-7 V=2,-7

Answer 2

`\(S'(-3, -5), \, T'(3, -3), \, U'(6, -1), \, V'(-2, 1)\)`.

To find the images of the vertices S, T, U, and V of Quadrilateral STUV after a reflection across the line
`\(y = -4\)`, we can use the formula for reflecting a point
`\((x, y)\)` across a horizontal line
`\(y = k\)`:

`\[ (x, y) \rightarrow (x, 2k - y) \]`

In this case, the line of reflection is
`\(y = -4\)`, so the formula becomes:

`\[ (x, y) \rightarrow (x, -8 - y) \]`

Now, apply this formula to each vertex:

1. S' ( _, _ )

For S(-3, -3):

`\[ S'(-3, -8 - (-3)) \]`

`\[ S'(-3, -5) \]`

2. T' ( _, _ )

For T(3, -5):

`\[ T'(3, -8 - (-5)) \]`

`\[ T'(3, -3) \]`

3. U' ( _, _ )

For U(6, -7):

`\[ U'(6, -8 - (-7)) \]`

`\[ U'(6, -1) \]`

4. V' ( _, _ )

For V(-2, -7):

`\[ V'(-2, -8 - (-7)) \]`

`\[ V'(-2, 1) \]`

Therefore, the images of the vertices after the reflection are:

`\[ S'(-3, -5), \, T'(3, -3), \, U'(6, -1), \, V'(-2, 1) \]`