Question

complete the table to show the coordinates of figure efgh and its image. figure efgh figure efgh e(-3,4) ? f(-1,4) e(3,4) g(-2,1) e(-3,4) h(-4,3) e(4,3) e(-4,3)

Explanation:

Step1: Analyze the transformation

Looking at the coordinates of \(F(-1,4)\) and \(F'(3,4)\). The \(y -\)coordinate remains the same (\(y = 4\)), and the \(x -\)coordinate changes. The transformation rule for a horizontal translation is \((x,y)\to(x + h,y)\). Here, \(h=3-(-1)=4\).

Step2: Apply the transformation rule to other points

For point \(E(-3,4)\):
Using the rule \((x,y)\to(x + 4,y)\), substitute \(x=-3\) and \(y = 4\).
\(x=-3 + 4=1\), \(y = 4\). So \(E'(1,4)\)
For point \(G(-2,1)\):
Substitute \(x=-2\) and \(y = 1\) into \((x,y)\to(x + 4,y)\)
\(x=-2+4 = 2\), \(y = 1\). So \(G'(2,1)\)
For point \(H(-4,3)\):
Substitute \(x=-4\) and \(y = 3\) into \((x,y)\to(x + 4,y)\)
\(x=-4 + 4=0\), \(y = 3\). So \(H'(0,3)\)

Answer:

Figure \(EFGH\)	Figure \(E'F'G'H'\)
\(F(-1,4)\)	\(F'(3,4)\)
\(G(-2,1)\)	\(G'(2,1)\)
\(H(-4,3)\)	\(H'(0,3)\)