izelissenpai
Answered

At Westonci.ca, we provide clear, reliable answers to all your questions. Join our vibrant community and get the solutions you need. Find reliable answers to your questions from a wide community of knowledgeable experts on our user-friendly Q&A platform. Get immediate and reliable solutions to your questions from a community of experienced professionals on our platform.

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.

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 Congru class=

Sagot :

Answers:

  1. True
  2. False
  3. True

==========================================================

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

[tex](x,y) \to (x+9,y-6)[/tex]

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.

-----------------------------------------------

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.

Thank you for choosing our platform. We're dedicated to providing the best answers for all your questions. Visit us again. We appreciate your time. Please come back anytime for the latest information and answers to your questions. Thank you for visiting Westonci.ca. Stay informed by coming back for more detailed answers.