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

By observing the coordinates of \(F(-1,4)\) and \(F'(3,4)\), we can find the transformation rule. The \(y -\)coordinate remains the same (\(y = 4\)), and for the \(x -\)coordinate: \(-1+4=3\). So the transformation is a translation \(4\) units to the right. The rule for a translation \(4\) units to the right is \((x,y)\to(x + 4,y)\).

Step2: Find the coordinates of \(E'\)

For point \(E(-3,4)\), using the rule \((x,y)\to(x + 4,y)\). Substitute \(x=-3\) and \(y = 4\) into the rule: \(x'=-3 + 4=1\), \(y'=4\). So \(E'(1,4)\).

Step3: Find the coordinates of \(G'\)

For point \(G(-2,1)\), using the rule \((x,y)\to(x + 4,y)\). Substitute \(x=-2\) and \(y = 1\) into the rule: \(x'=-2+4 = 2\), \(y'=1\). So \(G'(2,1)\).

Step4: Find the coordinates of \(H'\)

For point \(H(-4,3)\), using the rule \((x,y)\to(x + 4,y)\). Substitute \(x=-4\) and \(y = 3\) into the rule: \(x'=-4 + 4=0\), \(y'=3\). So \(H'(0,3)\).

Answer:

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