Question

graph the image of trapezoid stuv after a reflection over the line y = 1.

Explanation:

Step1: Find the coordinates of original points

The coordinates of the vertices of trapezoid \(STUV\) are \(S(-2,4)\), \(T(-2,9)\), \(U(6,7)\), \(V(6,5)\).

Step2: Use the reflection formula over \(y = 1\)

The formula for reflecting a point \((x,y)\) over the line \(y = k\) is \((x,2k - y)\). Here \(k = 1\), so the formula is \((x,2\times1 - y)=(x,2 - y)\).

• For \(S(-2,4)\):

\(x=-2\), \(y = 4\). The reflected point \(S'\) has coordinates \((-2,2-4)=(-2,-2)\)

• For \(T(-2,9)\):

\(x=-2\), \(y = 9\). The reflected point \(T'\) has coordinates \((-2,2 - 9)=(-2,-7)\)

• For \(U(6,7)\):

\(x = 6\), \(y=7\). The reflected point \(U'\) has coordinates \((6,2-7)=(6,-5)\)

• For \(V(6,5)\):

\(x = 6\), \(y = 5\). The reflected point \(V'\) has coordinates \((6,2-5)=(6,-3)\)

Step3: Plot the reflected points

Plot the points \(S'(-2,-2)\), \(T'(-2,-7)\), \(U'(6,-5)\), \(V'(6,-3)\) on the coordinate - plane and connect them in the same order as \(STUV\) (i.e., \(S'\to T'\to U'\to V'\to S'\)) to get the image of the trapezoid after reflection over \(y = 1\).

Answer:

The coordinates of the vertices of the reflected trapezoid are \(S'(-2,-2)\), \(T'(-2,-7)\), \(U'(6,-5)\), \(V'(6,-3)\). Plot these points and connect them to graph the reflected trapezoid.