Question

find the coordinates of the vertices after a translation 3 units right and 1 unit down.

Explanation:

1. First, identify the original coordinates of the vertices:

• Let's assume the coordinates of point \(E\) are \((-6,4)\), point \(F\) are \((-6,9)\), point \(G\) are \((2,9)\), and point \(H\) are \((2,4)\).
• The rule for a translation \(3\) units right and \(1\) unit down is \((x,y)\to(x + 3,y-1)\).

1. Calculate the new - coordinates for each vertex:

• For point \(E(-6,4)\):
• Apply the translation rule: \(x=-6\), \(y = 4\).
• \(x+3=-6 + 3=-3\), \(y - 1=4-1 = 3\). So the new coordinates of \(E\) are \((-3,3)\).
• For point \(F(-6,9)\):
• Apply the translation rule: \(x=-6\), \(y = 9\).
• \(x + 3=-6+3=-3\), \(y-1=9 - 1=8\). So the new coordinates of \(F\) are \((-3,8)\).
• For point \(G(2,9)\):
• Apply the translation rule: \(x = 2\), \(y = 9\).
• \(x+3=2 + 3=5\), \(y-1=9-1 = 8\). So the new coordinates of \(G\) are \((5,8)\).
• For point \(H(2,4)\):
• Apply the translation rule: \(x = 2\), \(y = 4\).
• \(x+3=2+3=5\), \(y-1=4 - 1=3\). So the new coordinates of \(H\) are \((5,3)\).

Step1: Identify original coordinates

Let \(E(-6,4)\), \(F(-6,9)\), \(G(2,9)\), \(H(2,4)\)

Step2: Apply translation rule for \(E\)

\((-6,4)\to(-6 + 3,4-1)=(-3,3)\)

Step3: Apply translation rule for \(F\)

\((-6,9)\to(-6 + 3,9-1)=(-3,8)\)

Step4: Apply translation rule for \(G\)

\((2,9)\to(2 + 3,9-1)=(5,8)\)

Step5: Apply translation rule for \(H\)

\((2,4)\to(2 + 3,4-1)=(5,3)\)

Answer:

The new coordinates of \(E\) are \((-3,3)\), of \(F\) are \((-3,8)\), of \(G\) are \((5,8)\), and of \(H\) are \((5,3)\)