Question

in the coordinate plane, the point ( x(-1,0) ) is translated to the point ( x(-2,2) ). under the same translation, the points ( y(-3,2) ) and ( z(3,-2) ) are translated to ( y ) and ( z ), respectively. what are the coordinates of ( y ) and ( z )?

Explanation:

Step1: Find the translation rule

The translation from \(X(-1,0)\) to \(X'(-2,2)\) is \((x,y)\to(x + a,y + b)\).
For the \(x\) - coordinate: \(-1+a=-2\), so \(a=-2 + 1=-1\).
For the \(y\) - coordinate: \(0 + b=2\), so \(b = 2\). The translation rule is \((x,y)\to(x-1,y + 2)\).

Step2: Translate point \(Y(-3,2)\)

Using the rule \((x,y)\to(x-1,y + 2)\), for \(Y(-3,2)\):
The \(x\) - coordinate of \(Y'\) is \(x=-3-1=-4\).
The \(y\) - coordinate of \(Y'\) is \(y=2 + 2=4\). So \(Y'(-4,4)\).

Step3: Translate point \(Z(3,-2)\)

Using the rule \((x,y)\to(x-1,y + 2)\), for \(Z(3,-2)\):
The \(x\) - coordinate of \(Z'\) is \(x=3-1 = 2\).
The \(y\) - coordinate of \(Z'\) is \(y=-2+2=0\). So \(Z'(2,0)\).

Answer:

\(Y'(-4,4)\) and \(Z'(2,0)\)