Question

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

Explanation:

Step1: Determine the translation rule

The \(x\)-coordinate of \(X(-4,0)\) changes to \(0\) (\(-4 + a=0\), so \(a = 4\)). The \(y\)-coordinate of \(X(0)\) changes to \(-2\) (\(0 + b=-2\), so \(b=-2\)). The translation rule is \((x,y)\to(x + 4,y-2)\)

Step2: Translate point \(Y(-2,-4)\)

For \(Y(-2,-4)\), using the rule \(x=-2+4\), \(y=-4 - 2\).
\(x = 2\), \(y=-6\)

Step3: Translate point \(Z(-7,2)\)

For \(Z(-7,2)\), using the rule \(x=-7 + 4\), \(y=2-2\)
\(x=-3\), \(y = 0\)

Answer:

\(Y'(2,-6)\)
\(Z'(-3,0)\)