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Point A(−3,2)

is to be reflected over the vertical line x=1
. What are the coordinates of the image of A′
?

1 answer

To reflect a point over a vertical line, you can follow these steps:

  1. Identify the original point: A(-3, 2).
  2. Identify the vertical line of reflection: x = 1.

The reflection of point A across the line x = 1 can be done by:

  • Finding the horizontal distance from the point A to the line x = 1:

    • The x-coordinate of point A is -3.
    • The distance from -3 to 1 is \(1 - (-3) = 1 + 3 = 4\).

  • Determine the x-coordinate of the reflected point (A'):

    • To find the coordinates of the reflected point A' across the line x = 1, you add the same distance from the line to get the new x-coordinate:
    • Start at the line x = 1 and move 4 units to the right:
    • \(1 + 4 = 5\).
  1. Keep the y-coordinate the same:
    • The y-coordinate of the point A remains unchanged since we are reflecting across a vertical line.
    • Thus, the y-coordinate of A' is still 2.

Putting this together, the coordinates of the image A' after reflection are (5, 2).

So, the coordinates of A' are \(\boxed{(5, 2)}\).