Question

in the coordinate plane, the point ( a(1,4) ) is translated to the point ( a(-3,-1) ). under the same translation, the points ( b(4,6) ) and ( c(5,8) ) 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 \(A'(-3,-1)\).
For the \(x\) - coordinate: \(-3 - 1=-4\).
For the \(y\) - coordinate: \(-1 - 4=-5\).
The translation rule is \((x,y)\to(x - 4,y - 5)\).

Step2: Apply the translation rule to point \(B(4,6)\)

For the \(x\) - coordinate of \(B'\): \(4-4 = 0\).
For the \(y\) - coordinate of \(B'\): \(6 - 5=1\).
So \(B'=(0,1)\).

Step3: Apply the translation rule to point \(C(5,8)\)

For the \(x\) - coordinate of \(C'\): \(5-4 = 1\).
For the \(y\) - coordinate of \(C'\): \(8 - 5=3\).
So \(C'=(1,3)\).

Answer:

\(B'(0,1)\) and \(C'(1,3)\)