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B (1,7) 5- 4- 3 2- 1- A (5,5) < (1 point) < x + 1 2 5 6 -0+ -10 -1- C (3,2) 3 4 Dilate the triangle using a magnitude of and a center of dilation at (2, 2) to form triangle A' B'C'. What are the coordinates of the dilated triangle? Α΄(8,8), Β΄(0,12), C'(4,2) Ο Α΄(7,7), Β΄(3,9), C'(5,4) Α΄(3.5,3.5), Β' (1.5,4.5), C'(2.5,2) Ο Α΄(2.5.2.5), Β΄(0.5,3.5), C'(1.5,1)

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To dilate the triangle with a center of dilation at (2, 2) and a magnitude of 2 (it appears that the magnitude is not explicitly stated but let's assume 2 for this example), we can use the following formula for dilation:

\[ (x', y') = (k(x - x_c) + x_c, k(y - y_c) + y_c) \]

where \( (x_c, y_c) \) is the center of dilation, \( k \) is the magnitude of the dilation, and \( (x', y') \) are the new coordinates after dilation.

Given the coordinates of the vertices of triangle ABC:

  • A(5, 5)
  • B(1, 7)
  • C(3, 2)

Let's perform the dilation for each vertex:

For point A(5, 5):

  • \( (x_c, y_c) = (2, 2) \)
  • \( k = 2 \)
  • New coordinates: \[ A' = (2 + 2(5 - 2), 2 + 2(5 - 2)) = (2 + 2 \cdot 3, 2 + 2 \cdot 3) = (2 + 6, 2 + 6) = (8, 8) \]

For point B(1, 7):

\[ B' = (2 + 2(1 - 2), 2 + 2(7 - 2)) = (2 + 2(-1), 2 + 2(5)) = (2 - 2, 2 + 10) = (0, 12) \]

For point C(3, 2):

\[ C' = (2 + 2(3 - 2), 2 + 2(2 - 2)) = (2 + 2(1), 2 + 2(0)) = (2 + 2, 2 + 0) = (4, 2) \]

Now we have the coordinates of the dilated triangle A' B' C':

  • A' (8, 8)
  • B' (0, 12)
  • C' (4, 2)

Therefore, the coordinates of the dilated triangle are:

A' (8, 8), B' (0, 12), C' (4, 2)

So the correct option is: Α΄(8,8), Β΄(0,12), C'(4,2).