Which sequence of transformations will map figure Q onto figure Q′?
Two congruent quadrilaterals are shown on a coordinate plane; quadrilateral Q with coordinates negative 9 comma 2, negative 6 comma 4, negative 4 comma 4, and negative 2 comma 2; quadrilateral Q prime with coordinates 2 comma 2, 4 comma 4, 6 comma 4, and 9 comma 2.
A) Translation of (x, y + 2), reflection over x = 1, and 180° rotation about the origin
B) Translation of (x, y − 2), reflection over x = 1, and 180° rotation about the origin
C) Translation of (x, y − 2), reflection over y = 1, and 180° rotation about the origin
D) Translation of (x, y + 2), reflection over y = 1, and 180° rotation about the origin
Answers
Answer:
Which sequence of transformations will map figure Q onto figure Q′?
Its D.Translation of (x, y + 2), reflection over y = 1, and 180° rotation about the origin
Step-by-step explanation:
The sequence of transformations that will map figure Q onto figure Q′ : 'Translation of (x, y + 2), reflection over y = 1, and 180° rotation about the origin.'
The correct answer is option (D)
What is translation?"It is a geometric transformation in which the displacement of a figure from one place to another."
What is reflection?"It is a geometric transformation where all the points of an object are reflected on the line of reflection."
What is rotation?"It is a transformation in which the object is rotated about a fixed point."
For given question,
Quadrilateral Q with coordinates (-9, 2) ,(-6, 4) ,(- 4, 4) , and (-2, 2) Quadrilateral Q' with coordinates (2, 2), (4, 4), (6, 4), and (9, 2)
Consider a point (-4, 4) of quadrilateral Q. If we reflect Q over x = 1, then it would push the x coordinate of (-4, 4) to new x value 5 units to the right of x = 1, which is x = 6, and 180 rotation would make x = -6 But x = -6 is not in Q' . So it must be reflection over y = 1.Consider the transformations at option C, First translate to (x, y - 2) So, the translation of (-4,4) becomes (-4, 2), reflection over y = 1 gives (-4, 4), and 180° rotation about origin gives (4, -4) which is not the coordinate of Q'Now, consider the translation of (x, y + 2) So, the translation of (-4, 4) becomes (-4, 6), reflection over y = 1 gives (-4, -4), and 180° rotation about origin gives (4, 4) which is the coordinate of Q'Therefore, the sequence of transformations that will map figure Q onto figure Q′ : 'Translation of (x, y + 2), reflection over y = 1, and 180° rotation about the origin'
The correct answer is option (D)
Learn more about geometric transformations here:
https://brainly.com/question/15577335
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Step 1: Subtract [tex]2[/tex] from both sides.
[tex]-2n = 3n + 17 - 2[/tex]
Step 2: Simplify [tex]3n + 17 - 2[/tex] to [tex]3n + 15[/tex].
[tex]-2n = 3n + 15[/tex]
Step 3: Subtract [tex]3n[/tex] from both sides.
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Step 4: Simplify [tex]-2n - 3n[/tex] to [tex]-5n[/tex].
[tex]-5n = 15[/tex]
Step 5: Divide both sides by [tex]-5[/tex].
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Step 6: Simplify [tex]-\frac{15}{5}[/tex] to [tex]-3[/tex].
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