Question

1. rotate △def 90 degrees clockwise around the origin. then translate △def to the right 5 units and down 2 units. what are the coordinates of the vertices of △def? show your work. 5. figures a and b are congruent. which sequences of transformations can you perform on figure a to show this? select all the correct answers. a reflect figure a across the y - axis. b rotate figure a 180° counterclockwise. c reflect figure a across the y - axis. then rotate figure a 180° clockwise. d reflect figure a across the x - axis. then rotate figure a 180° clockwise. e rotate figure a 180° clockwise. then reflect the image across the x - axis.

Explanation:

4.

Step1: Identify original coordinates

Assume \(D(- 5,-1)\), \(E(0, - 1)\), \(F(-3,-5)\).

Step2: Apply 90 - degree clockwise rotation rule \((x,y)\to(y,-x)\)

For \(D(-5,-1)\), new coordinates \(D'(-1,5)\); for \(E(0,-1)\), new coordinates \(E'(-1,0)\); for \(F(-3,-5)\), new coordinates \(F'(-5,3)\).

Step3: Apply translation rule \((x,y)\to(x + 5,y-2)\)

For \(D'(-1,5)\), new - coordinates \(D''(-1 + 5,5-2)=(4,3)\); for \(E'(-1,0)\), new coordinates \(E''(-1 + 5,0-2)=(4,-2)\); for \(F'(-5,3)\), new coordinates \(F''(-5 + 5,3-2)=(0,1)\).

Visualize the effects of each transformation on figure \(A\). A reflection across the \(y\) - axis changes the sign of the \(x\) - coordinate. A \(180^{\circ}\) rotation (clockwise or counter - clockwise) changes the signs of both \(x\) and \(y\) coordinates.

• Option A: Reflecting figure \(A\) across the \(y\) - axis will map it onto figure \(B\).
• Option B: Rotating figure \(A\) \(180^{\circ}\) counter - clockwise will not map it onto figure \(B\).
• Option C: Reflecting across the \(y\) - axis and then rotating \(180^{\circ}\) clockwise is equivalent to a single reflection across the \(y\) - axis in this case and will map figure \(A\) onto figure \(B\).
• Option D: Reflecting across the \(x\) - axis and then rotating \(180^{\circ}\) clockwise will not map figure \(A\) onto figure \(B\).
• Option E: Rotating \(180^{\circ}\) clockwise and then reflecting across the \(x\) - axis will not map figure \(A\) onto figure \(B\).

Answer:

The coordinates of \(D'\) are \((4,3)\), \(E'\) are \((4,-2)\) and \(F'\) are \((0,1)\)

5.