Question

graph the image of square j k l m after a reflection over the line x = - 1.

Explanation:

Step1: Find the coordinates of original points

From the graph, the coordinates of \(J(4,8)\), \(K(6,8)\), \(L(6,10)\), \(M(4,10)\)

Step2: Use the reflection formula over \(x = a\)

The formula for reflecting a point \((x,y)\) over the line \(x=a\) is \((2a - x,y)\). Here \(a=-1\)
For point \(J(4,8)\):
\(x'=2\times(-1)-4=-2 - 4=-6\), \(y' = 8\), so \(J'(-6,8)\)
For point \(K(6,8)\):
\(x'=2\times(-1)-6=-2-6 = -8\), \(y'=8\), so \(K'(-8,8)\)
For point \(L(6,10)\):
\(x'=2\times(-1)-6=-2 - 6=-8\), \(y'=10\), so \(L'(-8,10)\)
For point \(M(4,10)\):
\(x'=2\times(-1)-4=-2-4=-6\), \(y'=10\), so \(M'(-6,10)\)

Step3: Plot the new points

Plot \(J'(-6,8)\), \(K'(-8,8)\), \(L'(-8,10)\), \(M'(-6,10)\) and connect them to form the reflected square.

Answer:

The coordinates of the reflected square are \(J'(-6,8)\), \(K'(-8,8)\), \(L'(-8,10)\), \(M'(-6,10)\). Plot these points on the coordinate - plane and connect them to get the image of square \(JKLM\) after reflection over the line \(x = - 1\).