Question

graph the image of kite abcd after a reflection over the line $y = 3$.

Explanation:

Step1: Find coordinates of original points

Assume \(A(-1,-3)\), \(B(0,-3)\), \(C(-1,0)\), \(D(-3,-3)\)

Step2: Apply reflection formula

The formula for reflection over the line \(y = k\) is \((x,y)\to(x,2k - y)\). Here \(k = 3\), so \((x,y)\to(x,6 - y)\)

• For \(A(-1,-3)\): \(x=-1\), \(y = 6-(-3)=9\), new point \(A'(-1,9)\)
• For \(B(0,-3)\): \(x = 0\), \(y=6-(-3)=9\), new point \(B'(0,9)\)
• For \(C(-1,0)\): \(x=-1\), \(y=6 - 0=6\), new point \(C'(-1,6)\)
• For \(D(-3,-3)\): \(x=-3\), \(y=6-(-3)=9\), new point \(D'(-3,9)\)

Step3: Plot new points

Plot \(A'(-1,9)\), \(B'(0,9)\), \(C'(-1,6)\), \(D'(-3,9)\) and connect them to form the reflected kite.

Answer:

Plot the points \(A'(-1,9)\), \(B'(0,9)\), \(C'(-1,6)\), \(D'(-3,9)\) and connect them.