Question

question 3
vertex ( d(-2,3) ) is first reflected across the ( x )-axis, then rotated ( 90^{circ} ) counterclockwise around the origin, then translated 1 unit left and 2 units up. what are the final coordinates?
( (-2,0) )
( (0,2) )
( (4,-4) )
( (2,0) )
question 4
a quadrilateral vertex starts at ( (-1,4) ). it undergoes this sequence: reflect across the ( y )-axis, then rotate ( 90^{circ} ) clockwise around the origin. what are the final coordinates?
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Explanation:

Step1: Reflect across the x - axis

When reflecting a point \((x,y)\) across the \(x\) - axis, the rule is \((x,y)\to(x, - y)\).
For the point \(D(-2,3)\), after reflection across the \(x\) - axis, the new point is \((-2,-3)\).

Step2: Rotate \(90^{\circ}\) counter - clockwise around the origin

The rule for a \(90^{\circ}\) counter - clockwise rotation around the origin is \((x,y)\to(-y,x)\).
For the point \((-2,-3)\), after rotation, the new point is \((3,-2)\).

Step3: Translate 1 unit left and 2 units up

The rule for translation is \((x,y)\to(x - 1,y + 2)\).
For the point \((3,-2)\), after translation, the new point is \((3-1,-2 + 2)=(2,0)\).

Step1: Reflect across the y - axis

When reflecting a point \((x,y)\) across the \(y\) - axis, the rule is \((x,y)\to(-x,y)\).
For the point \((-1,4)\), after reflection across the \(y\) - axis, the new point is \((1,4)\).

Step2: Rotate \(90^{\circ}\) clockwise around the origin

The rule for a \(90^{\circ}\) clockwise rotation around the origin is \((x,y)\to(y,-x)\).
For the point \((1,4)\), after rotation, the new point is \((4,-1)\).

Answer:

\((2,0)\)

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