Question

the rectangle jklm, shown below, is translated 3 units to the right and 4 units down to form the image jklm.
draw
write the coordinates of the vertices of jklm.
show your work here

Explanation:

Step1: Determine the original coordinates

From the graph, the coordinates of the vertices of rectangle \(JKLM\) are \(J(6,2)\), \(K(6, - 3)\), \(L(-4,-3)\), \(M(-4,2)\).

Step2: Apply the translation rule

The translation rule is \((x,y)\to(x + 3,y-4)\).

• For point \(J(6,2)\):

\(x=6,y = 2\). After translation, \(x'=6 + 3=9\), \(y'=2-4=-2\). So \(J'(9,-2)\).

• For point \(K(6,-3)\):

\(x = 6,y=-3\). After translation, \(x'=6 + 3=9\), \(y'=-3-4=-7\). So \(K'(9,-7)\).

• For point \(L(-4,-3)\):

\(x=-4,y=-3\). After translation, \(x'=-4 + 3=-1\), \(y'=-3-4=-7\). So \(L'(-1,-7)\).

• For point \(M(-4,2)\):

\(x=-4,y = 2\). After translation, \(x'=-4+3=-1\), \(y'=2 - 4=-2\). So \(M'(-1,-2)\).

Answer:

The coordinates of the vertices of \(J'K'L'M'\) are \(J'(9,-2)\), \(K'(9,-7)\), \(L'(-1,-7)\), \(M'(-1,-2)\)