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: Recall reflection over x - axis rule

The rule for reflecting a point \((x,y)\) over the \(x\) - axis is \((x,y)\to(x, - y)\).

Step2: Recall translation rule (2 units up)

The rule for translating a point \((x,y)\) 2 units up is \((x,y)\to(x,y + 2)\).

Step3: Find \(A'\)

For point \(A(1,1)\):

• Reflect over \(x\) - axis: \((1,1)\to(1,-1)\)
• Translate 2 units up: \((1,-1)\to(1,-1 + 2)=(1,1)\)

So \(A'\) corresponds to \((1,1)\)

Step4: Find \(B'\)

For point \(B(2,3)\):

• Reflect over \(x\) - axis: \((2,3)\to(2,-3)\)
• Translate 2 units up: \((2,-3)\to(2,-3 + 2)=(2,-1)\)

So \(B'\) corresponds to \((2,-1)\)

Step5: Find \(C'\)

For point \(C(3,2)\):

• Reflect over \(x\) - axis: \((3,2)\to(3,-2)\)
• Translate 2 units up: \((3,-2)\to(3,-2 + 2)=(3,0)\)

So \(C'\) corresponds to \((3,0)\)

Step6: Find \(D'\)

For point \(D(2,1)\):

• Reflect over \(x\) - axis: \((2,1)\to(2,-1)\) (Wait, no, \(D(2,1)\) reflection over \(x\) - axis is \((2,-1)\), then translate 2 units up: \((2,-1)\to(2,-1 + 2)=(2,1)\)

So \(D'\) corresponds to \((2,1)\)

Answer:

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