Question

drag the tiles to the boxes to form correct pairs. not all tiles will be used.
the vertices of polygon abcd are at a(1, 1), b(2, 3), c(3, 2), and d(2, 1). abcd is reflected across the x - axis and translated 2 units up to form polygon abcd. match each vertex of polygon abcd to its coordinates.
(2, 1) a (1, 1) b (3, 0) c (2, 3) d
(-3, 4) (2, -1) (-2, 5)

Explanation:

Step1: Find the reflection across the x - axis

When a point \((x,y)\) is reflected across the \(x\) - axis, the rule is \((x,y)\to(x, - y)\).
For \(A(1,1)\): After reflection across the \(x\) - axis, \(A_1=(1,-1)\)
For \(B(2,3)\): After reflection across the \(x\) - axis, \(B_1=(2,-3)\)
For \(C(3,2)\): After reflection across the \(x\) - axis, \(C_1=(3,-2)\)
For \(D(2,1)\): After reflection across the \(x\) - axis, \(D_1=(2,-1)\)

Step2: Find the translation 2 units up

When a point \((x,y)\) is translated 2 units up, the rule is \((x,y)\to(x,y + 2)\)
For \(A_1(1,-1)\): After translation 2 units up, \(A'=(1,-1 + 2)=(1,1)\)
For \(B_1(2,-3)\): After translation 2 units up, \(B'=(2,-3+2)=(2,-1)\)
For \(C_1(3,-2)\): After translation 2 units up, \(C'=(3,-2 + 2)=(3,0)\)
For \(D_1(2,-1)\): After translation 2 units up, \(D'=(2,-1+2)=(2,1)\)

Answer:

\(A'\to(1,1)\), \(B'\to(2,-1)\), \(C'\to(3,0)\), \(D'\to(2,1)\)