Consider statements in the table shown. Select True or False for each statement about the sequences of transformations that can verify that square ABCD is congruent to square A'B'C'D'.
True False
Square ABCD is translated 9 units to the right, followed by a translation 6 units down.
Square ABCD is reflected across the y-axis, followed by a translation 6 units down.
Square ABCD is translated 6 units down, followed by a translation 9 units to the right.

Answers:

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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.

cosine

step-by-step explanation: