LT

Test: Coordinate transformations

Dynamic tasks on translation, reflection, transformation sequences and midpoints in the coordinate plane.

Question qty: 10
Duration in minutes: 18
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Time left: 00:00:00

Sample questions

  • Point A(x, y) is reflected in the y-axis. Find the image coordinates.
  • Find the midpoint of the segment with endpoints A(x1, y1) and B(x2, y2).
  • Point A(x, y) is translated twice by the same vector (dx, dy). Find the final coordinates.
  • Point A(x, y) is rotated 180° about the origin. Find its new coordinates.
  • Point A(x, y) is reflected in the x-axis. Find the image coordinates.
  • Point A(x, y) became A′(nx, ny). Which transformation explains this?
  • Point A(x, y) is translated by dx units in the x-direction and dy units in the y-direction. Find its new coordinates.
  • When a point is reflected in the y-axis, which coordinate changes sign?

Coordinate transformations

A translation moves every point by the same vector: (x, y) → (x + a, y + b). Reflection in the x-axis changes the sign of y, reflection in the y-axis changes x, and reflection in the origin changes both.

Sequences of transformations

Perform operations in the stated order and use each intermediate result in the next step. The midpoint is found by averaging the x-coordinates and the y-coordinates of the endpoints.