Question

write the coordinates of the vertices after a reflection over the x - axis.

Explanation:

1. Recall the rule for reflection over the \(x -\)axis:

• The rule for reflecting a point \((x,y)\) over the \(x -\)axis is \((x,y)\to(x, - y)\).

1. Identify the coordinates of the vertices before reflection:

• Assume the vertices of the shape in the graph are \(N(0,0)\), \(M(5,0)\), \(L(5, - 10)\), \(K(0,-10)\).

1. Apply the reflection rule to each vertex:

• For point \(N(0,0)\):
• Using the rule \((x,y)\to(x, - y)\), when \(x = 0\) and \(y = 0\), we have \((0,0)\to(0,0)\).
• For point \(M(5,0)\):
• Using the rule \((x,y)\to(x, - y)\), when \(x = 5\) and \(y = 0\), we have \((5,0)\to(5,0)\).
• For point \(L(5,-10)\):
• Using the rule \((x,y)\to(x, - y)\), when \(x = 5\) and \(y=-10\), we have \((5,-10)\to(5,10)\).
• For point \(K(0,-10)\):
• Using the rule \((x,y)\to(x, - y)\), when \(x = 0\) and \(y=-10\), we have \((0,-10)\to(0,10)\).

Answer:

The coordinates of the vertices after reflection over the \(x -\)axis are \(N(0,0)\), \(M(5,0)\), \(L(5,10)\), \(K(0,10)\)