Question

the rectangle lmno, shown below, is translated 5 units to the right and 3 units down to form the image lmno.

Explanation:

Step1: Determine the translation rule

The translation rule is \((x,y)\to(x + 5,y-3)\) since it is translated 5 units to the right (add 5 to \(x\)-coordinate) and 3 units down (subtract 3 from \(y\)-coordinate).

Step2: Find coordinates of \(L'\)

The coordinates of \(L\) are \((2,6)\). Using the rule: \(x=2 + 5=7\), \(y=6-3 = 3\). So \(L'=(7,3)\).

Step3: Find coordinates of \(M'\)

The coordinates of \(M\) are \((2,-5)\). Using the rule: \(x=2+5 = 7\), \(y=-5 - 3=-8\). So \(M'=(7,-8)\).

Step4: Find coordinates of \(N'\)

The coordinates of \(N\) are \((-6,-5)\). Using the rule: \(x=-6+5=-1\), \(y=-5 - 3=-8\). So \(N'=(-1,-8)\).

Step5: Find coordinates of \(O'\)

The coordinates of \(O\) are \((-6,6)\). Using the rule: \(x=-6 + 5=-1\), \(y=6-3 = 3\). So \(O'=(-1,3)\).

Answer:

\(L'(7,3)\), \(M'(7,-8)\), \(N'(-1,-8)\), \(O'(-1,3)\)