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Select the coordinates A' and I after dilation of the line segment AB with a scale factor of 2, centered at the origin where the endpoints are A (3,7) and B (4,9) (1 point)

A(6,3) and B (8,18)

A' (6,14) and B (8,18)

A (6,14) and B (-4,3)

A(3/2, 7/2) and B (2, 9/2)

1 answer

To find the coordinates after dilation of the line segment AB with a scale factor of 2 centered at the origin, we need to multiply each coordinate by the scale factor.

Given:

  • A(3, 7)
  • B(4, 9)

Using a scale factor of \( k = 2 \), the new coordinates (A' and B') will be:

  1. For point A: \[ A' = (2 \times 3, 2 \times 7) = (6, 14) \]

  2. For point B: \[ B' = (2 \times 4, 2 \times 9) = (8, 18) \]

Therefore, after dilation, the coordinates are:

  • A' (6, 14)
  • B' (8, 18)

The correct answer is: A' (6, 14) and B' (8, 18).