Question

in the coordinate plane, the point ( a(-2,3) ) is translated to the point ( a(0,0) ). under the same translation, the points ( b(-5,5) ) and ( c(-4,-1) ) are translated to ( b ) and ( c ), respectively. what are the coordinates of ( b ) and ( c )?

Explanation:

Step1: Find the translation rule

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

Step2: Apply the translation rule to point \(B(-5,5)\)

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

Step3: Apply the translation rule to point \(C(-4,-1)\)

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

Answer:

\(B'(-3,2)\) and \(C'(-2,-4)\)