Question

in the coordinate plane, the point ( x(4, - 1) ) is translated to the point ( x(1, 0) ). under the same translation, the points ( y(7, - 4) ) and ( z(8, - 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 \(X(4,-1)\) to \(X'(1,0)\).
For the \(x\) - coordinate: \(1 = 4 + a\), so \(a=1 - 4=-3\).
For the \(y\) - coordinate: \(0=-1 + b\), so \(b = 0+1 = 1\). The translation rule is \((x,y)\to(x - 3,y + 1)\).

Step2: Translate point \(Y(7,-4)\)

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

Step3: Translate point \(Z(8,-5)\)

For \(x\) - coordinate of \(Z'\): \(x=8-3 = 5\).
For \(y\) - coordinate of \(Z'\): \(y=-5 + 1=-4\). So \(Z'=(5,-4)\).

Answer:

\(Y'(4,-3)\) and \(Z'(5,-4)\)