Answers:
- True
- False
- True
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Explanation:
Point A is at (-3, 4). If we apply the translation rule of "shift 9 units to the right and 6 units down", then we apply this transformation
We add 9 to the x coordinate and subtract 6 from the y coordinate.
So (-3,4) becomes (-3+9, 4-6) = (6, -2) which is where point A' is located in the diagram. You should find that points B,C,D all map to B', C', D' following this same translation rule.
Therefore, statement 1 is true.
Statement 3 is the same idea, but the order has been swapped. The order doesn't matter in this case. So that makes statement 3 true as well.
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Statement 2 on the other hand is false
Why? Because a reflection reverses the orientation of a figure. Note how both squares ABCD and A'B'C'D' all go clockwise when we go through the alphabet (ie A to B to C to D).
If a reflection happened, then A'B'C'D' would go counterclockwise and show that the orientation has been swapped. I recommend drawing an analogue clock and going up to a mirror to see that the orientation has swapped.
To swap the orientation back, you need a second reflection. This shows that two reflections either lead to a translation or a rotation (depending if the mirror lines are parallel or not).
If you wanted, you could track to see where point B ends up if you follow statement 2. Point B is at (-1, 4). Reflect over the y axis to get to (1, 4). Then shift 6 units down to arrive at (1, -2) which is not the correct location of B'. The diagram shows B' is actually at (8, -2). So this is an alternative way to see how statement 2 is false.
