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Nina [5.8K]
3 years ago
5

The image of the point (2, 1) under a translation is (-3, -2). Find

Mathematics
1 answer:
nirvana33 [79]3 years ago
8 0

Answer:

(-7, -12)

Explanation:

The translation of (2, 1) to (-3, -2) is 5 units left and 3 and 3 units down

2 - 5 = -3, x-coordinate = -3

1 - 3 = -2, y-coordinate = -2

Thus that makes the coordinates (-3, -2)

So that is taking away 5 from the x-axis and 3 away from the y-axis

-2 - 5 = -7, x-coordinate = -7

-9 - 3 = -12, y-coordinate = -12

Thus, the answer is (-7, -12)

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Determine whether the statement is true or false. Justify your answers.
marusya05 [52]

Answer:

The graph of y = f(-x) is a reflection of the graph of y = f(x) in the x-axis. ⇒ False

The graph of y = -f(x) is a reflection of the graph of y = f(x) in the y-axis. ⇒ False

Step-by-step explanation:

<em>Let us explain the reflection about the axes</em>

  • If a graph is reflected about the x-axis, then the y-coordinates of all points on it will opposite in sign

Ex: if a point (2, -3) is on the graph of f(x), and f(x) is reflected about the x-axis, then the point will change to (2, 3)

  • That means reflection about the x-axis change the sign of y
  • y = f(x) → reflection about x-axis → y = -f(x)

  • If a graph is reflected about the y-axis, then the x-coordinates of all points on it will opposite in sign

Ex: if a point (-2, -5) is on the graph of f(x), and f(x) is reflected about the y-axis, then the point will change to (2, -5)

  • That means reflection about the y-axis change the sign of x
  • y = f(x) → reflection about y-axis → y = f(-x)

<em>Now let us answer our question</em>

The graph of y = f(-x) is a reflection of the graph of y = f(x) in the x-axis.

It is False because reflection about x-axis change sign of y

The graph of y = -f(x) is a reflection of the graph of y = f(x) in the x-axis

The graph of y = -f(x) is a reflection of the graph of y = f(x) in the y-axis.

It is False because reflection about y-axis change sign of x

The graph of y = f(-x) is a reflection of the graph of y = f(x) in the y-axis

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Answer:

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Step-by-step explanation:

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Answer:

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Step-by-step explanation:

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Answer:

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