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Trapezoid ABCD is shown on the graph. If the trapezoid is rotated 90 degrees

counterclockwise about the origin and the resulting image is translated 6
units left, what are the coordinates of C"?

Trapezoid ABCD is shown on the graph. If the trapezoid is rotated 90 degrees counterclockwise-example-1

1 Answer

7 votes

Answer:

The coordinates of C" are (-7, 4)

Explanation:

  • If the point (x, y) rotated about the origin by angle 90° counterclockwise, then its image is (-y, x)
  • If the point (x, y) translated horizontally to the left by h units, then its image is (x - h, y)

From the given figure

∵ ABCD is a trapezoid

∵ The coordinates of the ponit C are (4, 1)

∴ x = 4 and y = 1

∵ The trapezoid is rotated 90 degrees counterclockwise about the origin

→ By using the 1st rule above, change the sigh of y and switch them

∴ C' = (-y, x)

C' = (-1, 4)

∵ The resulting image is translated 6 units left

→ By using the 2nd rule above subtract the x-coordinate by 6

∴ C" = (x - h, y)

∵ h = 6

x = -1 and y = 4

∴ C" = (-1 - 6, 4)

C" = (-7, 4)

The coordinates of C" are (-7, 4)

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