Question

graph the image of square kl mn after a reflection over the line ( y=-1 ).

Explanation:

Step1: Find the distance from each point to the line \(y = - 1\)

For a point \((x,y)\), the distance from the point to the line \(y=-1\) is \(d=y - (-1)=y + 1\).

• For point \(K(-2,1)\): \(d=1-(-1)=2\)
• For point \(L(2,1)\): \(d=1-(-1)=2\)
• For point \(M(2,5)\): \(d=5-(-1)=6\)
• For point \(N(-2,5)\): \(d=5-(-1)=6\)

Step2: Reflect each point over the line \(y=-1\)

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

• For \(K(-2,1)\): \(x=-2\), \(y = 1\), the reflected point \(K'(-2,-2 - 1)=(-2,-3)\)
• For \(L(2,1)\): \(x = 2\), \(y=1\), the reflected point \(L'(2,-2 - 1)=(2,-3)\)
• For \(M(2,5)\): \(x = 2\), \(y = 5\), the reflected point \(M'(2,-2 - 5)=(2,-7)\)
• For \(N(-2,5)\): \(x=-2\), \(y = 5\), the reflected point \(N'(-2,-2 - 5)=(-2,-7)\)

Step3: Plot the reflected points

Plot the points \(K'(-2,-3)\), \(L'(2,-3)\), \(M'(2,-7)\) and \(N'(-2,-7)\) and connect them to form the reflected square.

Answer:

The reflected square has vertices \(K'(-2,-3)\), \(L'(2,-3)\), \(M'(2,-7)\) and \(N'(-2,-7)\)