Question

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

Explanation:

Step1: Find the translation rule

The translation from \(A(1,-4)\) to \(A'(2,-5)\).
For the \(x\) - coordinate: \(2 - 1=1\).
For the \(y\) - coordinate: \(-5-(-4)=-1\).
The translation rule is \((x,y)\to(x + 1,y-1)\).

Step2: Translate point \(B(-1,0)\)

Using the rule \((x,y)\to(x + 1,y - 1)\).
For \(x\) - coordinate of \(B'\): \(-1+1 = 0\).
For \(y\) - coordinate of \(B'\): \(0-1=-1\).
So \(B'=(0,-1)\).

Step3: Translate point \(C(3,-2)\)

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

Answer:

\(B'(0,-1)\) and \(C'(4,-3)\)