Question

in the coordinate plane, the point a(-3, -2) is translated to the point a(0, -1). under the same translation, the points b(-5, -5) and c(-7, -6) are translated to b and c, respectively. what are the coordinates of b and c?

Explanation:

Step1: Determine the translation rule

The translation from \(A(-3,-2)\) to \(A'(0,-1)\) is \((x,y)\to(x + 3,y+1)\) since \(0-(-3)=3\) (change in \(x\)-coordinate) and \(-1-(-2) = 1\) (change in \(y\)-coordinate).

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

For point \(B(-5,-5)\), using the rule \((x,y)\to(x + 3,y + 1)\), we have \(x=-5+3=-2\) and \(y=-5 + 1=-4\). So \(B'(-2,-4)\).

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

For point \(C(-7,-6)\), using the rule \((x,y)\to(x + 3,y + 1)\), we have \(x=-7+3=-4\) and \(y=-6+1=-5\). So \(C'(-4,-5)\).

Answer:

The coordinates of \(B'\) are \((-2,-4)\) and the coordinates of \(C'\) are \((-4,-5)\).