Rotate △ABC A = (5,-1) B = (5,-9) C = (2,-7) 90 degrees (counterclockwise) about the origin to create △A′B′C′ . What are the coordinates of the following points?

Answer 1

To rotate a point \((x, y)\) 90 degrees counterclockwise about the origin, you can use the following transformation:

\[ (x, y) \to (-y, x) \]

Let's apply this transformation to each vertex of triangle \(\triangle ABC\).

1. For point \(A = (5, -1)\): \[ A' = (-(-1), 5) = (1, 5) \]

2. For point \(B = (5, -9)\): \[ B' = (-(-9), 5) = (9, 5) \]

3. For point \(C = (2, -7)\): \[ C' = (-(-7), 2) = (7, 2) \]

So, the coordinates of the rotated points are:

• \(A' = (1, 5)\)
• \(B' = (9, 5)\)
• \(C' = (7, 2)\)

Thus, the coordinates of triangle \(\triangle A'B'C'\) are:

• \(A' = (1, 5)\)
• \(B' = (9, 5)\)
• \(C' = (7, 2)\)

Answer 2

Now reflect △A′B′C′ across the y-axis to create △A"B"C" . What are the new coordinates?(3

Answer 3

To reflect a point \((x, y)\) across the y-axis, the transformation is:

\[ (x, y) \to (-x, y) \]

Let's apply this transformation to the points \(A' = (1, 5)\), \(B' = (9, 5)\), and \(C' = (7, 2)\) to find the coordinates of \(\triangle A''B''C''\).

1. For point \(A' = (1, 5)\): \[ A'' = (-1, 5) \]

2. For point \(B' = (9, 5)\): \[ B'' = (-9, 5) \]

3. For point \(C' = (7, 2)\): \[ C'' = (-7, 2) \]

So, the coordinates of the reflected points are:

• \(A'' = (-1, 5)\)
• \(B'' = (-9, 5)\)
• \(C'' = (-7, 2)\)

Thus, the coordinates of triangle \(\triangle A''B''C''\) are:

• \(A'' = (-1, 5)\)
• \(B'' = (-9, 5)\)
• \(C'' = (-7, 2)\)

Answer 4

Now reflect △A′B′C′ across the y-axis to create △A"B"C" . What are the new coordinates? A' = (1, 5) B' = (9, 5) C' = (7, 2)

Answer 5

To reflect a point \((x, y)\) across the y-axis, you use the transformation:

\[ (x, y) \to (-x, y) \]

Let's apply this transformation to the points \(A' = (1, 5)\), \(B' = (9, 5)\), and \(C' = (7, 2)\) to find the coordinates of the new triangle \(\triangle A''B''C''\).

1. For point \(A' = (1, 5)\): \[ A'' = (-1, 5) \]

2. For point \(B' = (9, 5)\): \[ B'' = (-9, 5) \]

3. For point \(C' = (7, 2)\): \[ C'' = (-7, 2) \]

So, the new coordinates after reflecting across the y-axis are:

• \(A'' = (-1, 5)\)
• \(B'' = (-9, 5)\)
• \(C'' = (-7, 2)\)

Thus, the coordinates of triangle \(\triangle A''B''C''\) are:

• \(A'' = (-1, 5)\)
• \(B'' = (-9, 5)\)
• \(C'' = (-7, 2)\)