Question

in the coordinate plane, the point ( a(-4,-1) ) is translated to the point ( a(-3,4) ). under the same translation, the points ( b(-7,-5) ) and ( c(-6,-4) ) are translated to ( b ) and ( c ), respectively. what are the coordinates of ( b ) and ( c )?

Explanation:

Step1: Determine the translation rule

The translation from \(A(-4,-1)\) to \(A'(-3,4)\).
For the \(x\) - coordinate: \(-3-(-4)=1\).
For the \(y\) - coordinate: \(4 - (-1)=5\).
The translation rule is \((x,y)\to(x + 1,y+5)\).

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

For point \(B(-7,-5)\), using the rule \((x,y)\to(x + 1,y + 5)\).
\(x=-7+1=-6\), \(y=-5 + 5=0\). So \(B'(-6,0)\).

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

For point \(C(-6,-4)\), using the rule \((x,y)\to(x + 1,y + 5)\).
\(x=-6+1=-5\), \(y=-4 + 5=1\). So \(C'(-5,1)\).

Answer:

The coordinates of \(B'\) are \((-6,0)\) and the coordinates of \(C'\) are \((-5,1)\)