Question

write the coordinates of the vertices after a translation 5 units right and 1 unit up.

Explanation:

Step1: Recall the translation rule

For a translation \(5\) units right and \(1\) unit up, the rule is \((x,y)\to(x + 5,y+1)\).

Step2: Apply the rule to each vertex

• For vertex \(U(-2,-2)\):

\(x=-2,y = - 2\). After translation, \(x'=-2 + 5=3,y'=-2 + 1=-1\). So \(U'=(3,-1)\).

• For vertex \(R(-2,-8)\):

\(x=-2,y=-8\). After translation, \(x'=-2 + 5 = 3,y'=-8+1=-7\). So \(R'=(3,-7)\).

• For vertex \(S(5,-8)\):

\(x = 5,y=-8\). After translation, \(x'=5 + 5=10,y'=-8 + 1=-7\). So \(S'=(10,-7)\).

• For vertex \(T(5,-2)\):

\(x = 5,y=-2\). After translation, \(x'=5+5 = 10,y'=-2 + 1=-1\). So \(T'=(10,-1)\).

Answer:

The coordinates of the vertices after translation are \(U'(3,-1)\), \(R'(3,-7)\), \(S'(10,-7)\), \(T'(10,-1)\)