Question

graph the image of square tuvw after a reflection over the line y = 1.

Explanation:

Step1: Find coordinates of original points

Assume \( T(0,3) \), \( U(6,3) \), \( V(6,9) \), \( W(0,9) \).

Step2: Use reflection formula

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

For point \(T(0,3)\)

Substitute \(x = 0\), \(y = 3\) into \((x,2 - y)\):
\((0,2-3)=(0,-1)\)

For point \(U(6,3)\)

Substitute \(x = 6\), \(y = 3\) into \((x,2 - y)\):
\((6,2 - 3)=(6,-1)\)

For point \(V(6,9)\)

Substitute \(x = 6\), \(y = 9\) into \((x,2 - y)\):
\((6,2-9)=(6,-7)\)

For point \(W(0,9)\)

Substitute \(x = 0\), \(y = 9\) into \((x,2 - y)\):
\((0,2 - 9)=(0,-7)\)

Step3: Plot new points

Plot \(T'(0,-1)\), \(U'(6,-1)\), \(V'(6,-7)\), \(W'(0,-7)\) and connect them to form the reflected square.

Answer:

Plot the points \(T'(0,-1)\), \(U'(6,-1)\), \(V'(6,-7)\), \(W'(0,-7)\) on the coordinate - plane and connect them.