Question

in the coordinate plane, the point ( x(-4,-2) ) is translated to the point ( x(0,1) ). under the same translation, the points ( y(-7,0) ) and ( z(-2,-4) ) are translated to ( y ) and ( z ), respectively. what are the coordinates of ( y ) and ( z )?

Explanation:

Step1: Find the translation rule

To find the translation rule, we compare the coordinates of \(X(-4,-2)\) and \(X'(0,1)\).
For the \(x\) - coordinate: \(0-(-4)=4\).
For the \(y\) - coordinate: \(1 - (-2)=3\).
The translation rule is \((x,y)\to(x + 4,y+3)\)

Step2: Translate point \(Y(-7,0)\)

Using the translation rule \((x,y)\to(x + 4,y + 3)\)
For \(x=-7\), \(x'=-7 + 4=-3\)
For \(y = 0\), \(y'=0+3=3\)
So \(Y'(-3,3)\)

Step3: Translate point \(Z(-2,-4)\)

Using the translation rule \((x,y)\to(x + 4,y + 3)\)
For \(x=-2\), \(x'=-2+4 = 2\)
For \(y=-4\), \(y'=-4 + 3=-1\)
So \(Z'(2,-1)\)

Answer:

\(Y'(-3,3)\) and \(Z'(2,-1)\)