Question

in the coordinate plane, the point ( x(3,1) ) is translated to the point ( x(5,0) ). under the same translation, the points ( y(5,4) ) and ( z(0,5) ) are translated to ( y ) and ( z ), respectively. what are the coordinates of ( y ) and ( z )?

Explanation:

Step1: Find the translation rule

The translation from \(X(3,1)\) to \(X'(5,0)\).
For the \(x\) - coordinate: \(5 - 3=2\).
For the \(y\) - coordinate: \(0 - 1=-1\).
The translation rule is \((x,y)\to(x + 2,y-1)\).

Step2: Translate point \(Y(5,4)\)

For the \(x\) - coordinate of \(Y'\): \(5+2 = 7\).
For the \(y\) - coordinate of \(Y'\): \(4-1 = 3\).
So \(Y'=(7,3)\).

Step3: Translate point \(Z(0,5)\)

For the \(x\) - coordinate of \(Z'\): \(0 + 2=2\).
For the \(y\) - coordinate of \(Z'\): \(5-1 = 4\).
So \(Z'=(2,4)\).

Answer:

\(Y'=(7,3)\) and \(Z'=(2,4)\)