Question

in the coordinate plane, the point ( a(1,-4) ) is translated to the point ( a(6,1) ). under the same translation, the points ( b(3,-6) ) and ( c(-2,-8) ) are translated to ( b ) and ( c ), respectively. what are the coordinates of ( b ) and ( c )?

Explanation:

Step1: Find the translation rule

The translation from \(A(1,-4)\) to \(A'(6,1)\).
For the \(x\) - coordinate: \(6 - 1=5\).
For the \(y\) - coordinate: \(1-(-4)=1 + 4 = 5\).
The translation rule is \((x,y)\to(x + 5,y+5)\).

Step2: Apply the translation rule to point \(B\)

For point \(B(3,-6)\), using the rule \((x,y)\to(x + 5,y + 5)\).
The \(x\) - coordinate of \(B'\) is \(3+5 = 8\).
The \(y\) - coordinate of \(B'\) is \(-6 + 5=-1\).
So \(B'=(8,-1)\).

Step3: Apply the translation rule to point \(C\)

For point \(C(-2,-8)\), using the rule \((x,y)\to(x + 5,y + 5)\).
The \(x\) - coordinate of \(C'\) is \(-2+5 = 3\).
The \(y\) - coordinate of \(C'\) is \(-8 + 5=-3\).

Answer:

\(B'(8,-1)\), \(C'(3,-3)\)