Question

show how each vertex of \\( \triangle efg \\) maps to its image. describe in words how to map \\( \triangle efg \\) to its image \\( \triangle efg \\) using a reflection. complete the table with the coordinates of the image points \\( e, f \\), and \\( g \\) (type ordered pairs.)

Explanation:

Step1: Determine the reflection rule

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

Step2: Apply the rule to each vertex

• For point \(E(-4,5)\):

Using the rule \((x,y)\to(x, - y)\), we substitute \(x=-4\) and \(y = 5\). So \(E'(-4,-5)\)

• For point \(F(-2,5)\):

Using the rule \((x,y)\to(x, - y)\), we substitute \(x=-2\) and \(y = 5\). So \(F'(-2,-5)\)

• For point \(G(-3,2)\):

Using the rule \((x,y)\to(x, - y)\), we substitute \(x=-3\) and \(y = 2\). So \(G'(-3,-2)\)

Answer:

\(E'(-4,-5)\), \(F'(-2,-5)\), \(G'(-3,-2)\)