Parallelogram A B C D is transformed to create parallelogram A apostrophe B apostrophe C apostrophe D apostrophe. Which shows the sequence of transformations needed to create A apostrophe B apostrophe C apostrophe D apostrophe ?
A graph is shown in the xy-plane. The values on the x-axis and the y-axis ranges from negative 8 to 8 in an increment of 2. The two parallelograms UpperWord ABCD and UpperWord A'B'C'D' are shown. The coordinates of the trapezium UpperWord ABCD are Upper A(negative 7, 1), Upper B(negative 6, 4), Upper C(negative 4, 4) and Upper D(negative 5, 1). The coordinates of the trapezium UpperWord A'B'C'D' are Upper A' (negative 7.5, 1.5), Upper B'(negative 6, 6), Upper C'(negative 3, 6) and Upper D'(negative 4.5, 1.5).
A
a dilation about the origin by a factor of 2 over 3 and a translation 3 units to the left
B
a dilation about the origin by a factor of 3 over 2 and a translation 3 units to the right
C
a dilation about the origin by a factor of 2 over 3 and a translation 3 units to the right
D
a dilation about the origin by a factor of 3 over 2 and a translation 3 units to the left
To determine the correct sequence of transformations that were applied to parallelogram ABCD to create A'B'C'D', we need to analyze the given information.
The coordinates of ABCD are:
A(-7, 1)
B(-6, 4)
C(-4, 4)
D(-5, 1)
The coordinates of A'B'C'D' are:
A'(-7.5, 1.5)
B'(-6, 6)
C'(-3, 6)
D'(-4.5, 1.5)
We observe that the x-coordinates of A'B'C'D' are obtained by applying a dilation about the origin by a factor of 2/3 to the x-coordinates of ABCD. This means that all x-values are multiplied by 2/3.
We also notice that the y-coordinates of A'B'C'D' are obtained by applying a dilation about the origin by a factor of 2/3 to the y-coordinates of ABCD. This means that all y-values are multiplied by 2/3.
So, applying a dilation about the origin by a factor of 2/3 transforms ABCD into a new parallelogram with vertices A"(x, y), B"(x, y), C"(x, y), and D"(x, y).
Now, translating this new parallelogram 3 units to the left corresponds to subtracting 3 from all x-coordinates. Therefore, the x-values of ABCD' will be obtained by subtracting 3 from the x-values of A"B"C"D".
The final result is parallelogram A'B'C'D'.
Based on these observations, the correct sequence of transformations needed to create A'B'C'D' is:
A dilation about the origin by a factor of 2/3 (to get A"B"C"D")
A translation 3 units to the left (to get ABCD').
Therefore, the correct answer is: A) a dilation about the origin by a factor of 2/3 and a translation 3 units to the left.
you know, your keyboard has an apostrophe key. Reading this dictation garbage sure gets old in a hurry.
Try typing A'B'C'D' and maybe you will get someone to help you.
Or, try the various transformations. Which sequence works?
IS A'B'C'D' bigger than ABCD? That will narrow your choices by half.
Then cut out a copy of the picture, and move it as needed.