Question

drag the tiles to the correct boxes to complete the pairs. not all tiles will be used.quadrilateral ( j k l m ) has vertices ( j(8,4), k(4,10), l(12,12) ), and ( m(14,10) ). match each quadrilateral, described by its vertices, to the sequence of transformations that will show it is congruent to quadrilateral ( j k l m ).
( s(4,16), t(10,20), u(12,12) ), and ( v(10,10) )
( e(5,6), f(1,12), g(9,14) ), and ( h(11,12) )
( w(5,1), x(1,7), y(9,9) ), and ( z(11,7) )
( o(10,1), p(6,7), q(14,9) ), and ( r(16,7) )
( a(-8,-4), b(-4,-10), c(-12,-12) ), and ( d(-14,-10) )
a translation 3 units left and 2 units up
a translation 2 units right and 3 units down
a sequence of reflections across the ( x ) - and ( y ) - axes, in any order
a translation 3 units down and 3 units left

Explanation:

Step1: Analyze translation 3 units left and 2 units up

For a point \((x,y)\), the transformation rule is \((x - 3,y+2)\).

• \(J(8,4)\): \(8-3 = 5\), \(4 + 2=6\)
• \(K(4,10)\): \(4-3 = 1\), \(10 + 2 = 12\)
• \(L(12,12)\): \(12-3=9\), \(12 + 2 = 14\)
• \(M(14,10)\): \(14-3 = 11\), \(10+2 = 12\)

The new vertices are \(E(5,6)\), \(F(1,12)\), \(G(9,14)\), \(H(11,12)\)

Step2: Analyze translation 2 units right and 3 units down

For a point \((x,y)\), the transformation rule is \((x + 2,y-3)\).

• \(J(8,4)\): \(8+2=10\), \(4-3 = 1\)
• \(K(4,10)\): \(4+2 = 6\), \(10-3=7\)
• \(L(12,12)\): \(12 + 2=14\), \(12-3 = 9\)
• \(M(14,10)\): \(14+2=16\), \(10-3 = 7\)

The new vertices are \(O(10,1)\), \(P(6,7)\), \(Q(14,9)\), \(R(16,7)\)

Step3: Analyze sequence of reflections across the \(x -\) and \(y -\) axes (in any order)

The rule for reflection across \(x -\) axis is \((x,-y)\), and then across \(y -\) axis is \((-x,-y)\) (or vice - versa).

• \(J(8,4)\): \((-8,-4)\)
• \(K(4,10)\): \((-4,-10)\)
• \(L(12,12)\): \((-12,-12)\)
• \(M(14,10)\): \((-14,-10)\)

The new vertices are \(A(-8,-4)\), \(B(-4,-10)\), \(C(-12,-12)\), \(D(-14,-10)\)

Step4: Analyze translation 3 units down and 3 units left

For a point \((x,y)\), the transformation rule is \((x-3,y - 3)\).

• \(J(8,4)\): \(8-3=5\), \(4-3 = 1\)
• \(K(4,10)\): \(4-3 = 1\), \(10-3=7\)
• \(L(12,12)\): \(12-3 = 9\), \(12-3=9\)
• \(M(14,10)\): \(14-3 = 11\), \(10-3 = 7\)

The new vertices are \(W(5,1)\), \(X(1,7)\), \(Y(9,9)\), \(Z(11,7)\)

Answer:

• a translation 3 units left and 2 units up: \(E(5,6)\), \(F(1,12)\), \(G(9,14)\), \(H(11,12)\)
• a translation 2 units right and 3 units down: \(O(10,1)\), \(P(6,7)\), \(Q(14,9)\), \(R(16,7)\)
• a sequence of reflections across the \(x -\) and \(y -\) axes, in any order: \(A(-8,-4)\), \(B(-4,-10)\), \(C(-12,-12)\), \(D(-14,-10)\)
• a translation 3 units down and 3 units left: \(W(5,1)\), \(X(1,7)\), \(Y(9,9)\), \(Z(11,7)\)