Question

given the following translation rule, write the ordered pair of a rule (x,y) → (x + 8, y + 2) a(8, -8) → ____ given the following translation rule, write the ordered pair of b rule (x,y) → (x - 7, y + 8) b(40, -9) → __ given the following translation rule, write the ordered pair of c rule (x,y) → (x + 1, y + 8) c(3, -7) → __ given the following translation rule, write the ordered pair of d rule (x,y) → (x + 6, y + 6) d(8, 3) → __ given the following translation rule, write the ordered pair of e rule (x,y) → (x + 10, y) e(0, 43) → __ given the following translation rule, write the ordered pair of f rule (x,y) → (x - 9, y + 3) f(9, -5) → ____

Explanation:

Step1: Calculate \(A'(x,y)\)

Given \(A(2,-8)\) and rule \((x,y)\to(x + 6,y+2)\).
For \(x\)-coordinate: \(2+6 = 8\).
For \(y\)-coordinate: \(-8 + 2=-6\). So \(A'(8,-6)\).

Step2: Calculate \(B'(x,y)\)

Given \(B(2,-8)\) and rule \((x,y)\to(x,y + 9)\).
For \(x\)-coordinate: \(2\).
For \(y\)-coordinate: \(-8+9 = 1\). So \(B'(2,1)\).

Step3: Calculate \(C'(x,y)\)

Given \(C(0,-7)\) and rule \((x,y)\to(x + 1,y+8)\).
For \(x\)-coordinate: \(0 + 1=1\).
For \(y\)-coordinate: \(-7+8 = 1\). So \(C'(1,1)\).

Step4: Calculate \(D'(x,y)\)

Given \(D(4,-9)\) and rule \((x,y)\to(x - 2,y+8)\).
For \(x\)-coordinate: \(4-2 = 2\).
For \(y\)-coordinate: \(-9+8=-1\). So \(D'(2,-1)\).

Step5: Calculate \(E'(x,y)\)

Given \(E(-14,5)\) and rule \((x,y)\to(-x,y)\).
For \(x\)-coordinate: \(-(-14)=14\).
For \(y\)-coordinate: \(5\). So \(E'(14,5)\).

Step6: Calculate \(F'(x,y)\)

Given \(F(-9,-5)\) and rule \((x,y)\to(x - 9,y+3)\).
For \(x\)-coordinate: \(-9-9=-18\).
For \(y\)-coordinate: \(-5 + 3=-2\). So \(F'(-18,-2)\).

Step7: Calculate \(G'(x,y)\)

Given \(G(0,4)\) and rule \((x,y)\to(x + 10,y)\).
For \(x\)-coordinate: \(0+10 = 10\).
For \(y\)-coordinate: \(4\). So \(G'(10,4)\).

Step8: Calculate \(H'(x,y)\)

Given \(H(8,3)\) and rule \((x,y)\to(x + 6,y+0)\).
For \(x\)-coordinate: \(8+6 = 14\).
For \(y\)-coordinate: \(3\). So \(H'(14,3)\).

Answer:

\(A'(8,-6)\), \(B'(2,1)\), \(C'(1,1)\), \(D'(2,-1)\), \(E'(14,5)\), \(F'(-18,-2)\), \(G'(10,4)\), \(H'(14,3)\)