Question

directions: graph and label each figure and its image under the given translation. give the new coor

1. rectangle qrst with vertices q(-6, -1), r(-3, 1),

s(1, -5), and t(-2, -7): (x, y)→(x + 5, y + 7)

1. triangle cde with vertices c(2, -1), d(7, -4),

and e(4, -6): (x, y)→(x - 3, y + 8)

1. rhombus jklm with vertices j(-4, 7), k(0, 8),

l(-1, 4), and m(-5, 3): (x, y)→(x + 2, y - 2)

1. square wxyz with vertices w(1, 7), x(6, 5),

y(4, 0), and z(-1, 2): (x, y)→(x - 7, y - 6)

1. triangle stu with vertices s(-4, 2), t(5, -1),

and u(-2, -2): (x, y)→(x - 1, y - 5)

1. trapezoid abcd with vertices a(-3, 6), b(0, 7),

c(1, 4), and d(-5, 2): (x, y)→(x + 4, y - 1)

Explanation:

Step1: Apply translation rule to each vertex

For each figure, take the \(x\) - coordinate and \(y\) - coordinate of each vertex and apply the given translation rule \((x,y)\to(x + a,y + b)\) (where \(a\) and \(b\) are constants from the rule).

For problem 1: \((x,y)\to(x + 5,y+7)\)

• For \(Q(-6,-1)\): \(x=-6+5=-1\), \(y=-1 + 7 = 6\), so \(Q'(-1,6)\)
• For \(R(-3,1)\): \(x=-3+5 = 2\), \(y=1 + 7=8\), so \(R'(2,8)\)
• For \(S(1,-5)\): \(x=1+5 = 6\), \(y=-5 + 7=2\), so \(S'(6,2)\)
• For \(T(-2,-7)\): \(x=-2+5 = 3\), \(y=-7 + 7=0\), so \(T'(3,0)\)

For problem 2: \((x,y)\to(x - 3,y + 8)\)

• For \(C(2,-1)\): \(x=2-3=-1\), \(y=-1 + 8 = 7\), so \(C'(-1,7)\)
• For \(D(7,-4)\): \(x=7-3 = 4\), \(y=-4 + 8=4\), so \(D'(4,4)\)
• For \(E(4,-6)\): \(x=4-3 = 1\), \(y=-6 + 8=2\), so \(E'(1,2)\)

For problem 3: \((x,y)\to(x + 2,y-2)\)

• For \(J(-4,7)\): \(x=-4+2=-2\), \(y=7-2 = 5\), so \(J'(-2,5)\)
• For \(K(0,8)\): \(x=0+2 = 2\), \(y=8-2=6\), so \(K'(2,6)\)
• For \(L(-1,4)\): \(x=-1+2 = 1\), \(y=4-2=2\), so \(L'(1,2)\)
• For \(M(-5,3)\): \(x=-5+2=-3\), \(y=3-2 = 1\), so \(M'(-3,1)\)

For problem 4: \((x,y)\to(x - 7,y-6)\)

• For \(W(1,7)\): \(x=1-7=-6\), \(y=7-6 = 1\), so \(W'(-6,1)\)
• For \(X(6,5)\): \(x=6-7=-1\), \(y=5-6=-1\), so \(X'(-1,-1)\)
• For \(Y(4,0)\): \(x=4-7=-3\), \(y=0-6=-6\), so \(Y'(-3,-6)\)
• For \(Z(-1,2)\): \(x=-1-7=-8\), \(y=2-6=-4\), so \(Z'(-8,-4)\)

For problem 5: \((x,y)\to(x - 1,y-5)\)

• For \(S(-4,2)\): \(x=-4-1=-5\), \(y=2-5=-3\), so \(S'(-5,-3)\)
• For \(T(5,-1)\): \(x=5-1 = 4\), \(y=-1-5=-6\), so \(T'(4,-6)\)
• For \(U(-2,-2)\): \(x=-2-1=-3\), \(y=-2-5=-7\), so \(U'(-3,-7)\)

For problem 6: \((x,y)\to(x + 4,y-1)\)

• For \(A(-3,6)\): \(x=-3+4 = 1\), \(y=6-1 = 5\), so \(A'(1,5)\)
• For \(B(0,7)\): \(x=0+4 = 4\), \(y=7-1=6\), so \(B'(4,6)\)
• For \(C(1,4)\): \(x=1+4 = 5\), \(y=4-1=3\), so \(C'(5,3)\)
• For \(D(-5,2)\): \(x=-5+4=-1\), \(y=2-1 = 1\), so \(D'(-1,1)\)

Answer:

1. \(Q'(-1,6)\), \(R'(2,8)\), \(S'(6,2)\), \(T'(3,0)\)
2. \(C'(-1,7)\), \(D'(4,4)\), \(E'(1,2)\)
3. \(J'(-2,5)\), \(K'(2,6)\), \(L'(1,2)\), \(M'(-3,1)\)
4. \(W'(-6,1)\), \(X'(-1,-1)\), \(Y'(-3,-6)\), \(Z'(-8,-4)\)
5. \(S'(-5,-3)\), \(T'(4,-6)\), \(U'(-3,-7)\)
6. \(A'(1,5)\), \(B'(4,6)\), \(C'(5,3)\), \(D'(-1,1)\)