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Coordinate transformations
Dynamic tasks on translation, reflection, transformation sequences and midpoints in the coordinate plane.
Questions: 10Estimated time: 17 minutes
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Question 1out of 10
Point A(-1, 4) is translated twice by the same vector (3, 2). Find the final coordinates.
Two identical translations give twice the vector. Add 2 × dx to x and 2 × dy to y: the final point is (x + 2dx, y + 2dy).
Question 2out of 10
Find the midpoint of the segment with endpoints A(-9, 3) and B(1, 9).
Find midpoint coordinates by averaging the endpoint coordinates separately: x = (x1 + x2) ÷ 2, y = (y1 + y2) ÷ 2. Keep negative signs when adding.
Question 3out of 10
Point A(1, -2) became A′(6, 1). Which transformation explains this?
Compare the initial and final coordinates. Reflection in the x-axis changes only the sign of y; reflection in the y-axis changes only x; a 180° rotation about the origin changes both signs.
Question 4out of 10
Point A(2, -3) is reflected in the y-axis. Find the image coordinates.
Reflection in the y-axis preserves y and reverses the sign of x: (x, y) → (−x, y). The image is the same distance on the other side of the vertical axis.
Question 5out of 10
Point A(-8, -7) is translated by 3 units in the x-direction and 0 units in the y-direction. Find its new coordinates.
Add the translation vector coordinates to the point coordinates: (x, y) → (x + dx, y + dy). Negative dx moves left and negative dy moves down.
Question 6out of 10
Point A(-3, 4) is reflected in the x-axis. Find the image coordinates.
Reflection in the x-axis preserves x and reverses the sign of y: (x, y) → (x, −y). The image is the same distance on the other side of the horizontal axis.
Question 7out of 10
Point A(9, 8) is reflected in the x-axis. Find the image coordinates.
Reflection in the x-axis preserves x and reverses the sign of y: (x, y) → (x, −y). The image is the same distance on the other side of the horizontal axis.
Question 8out of 10
Point A(-2, 2) became A′(3, 5). Which transformation explains this?
Compare the initial and final coordinates. Reflection in the x-axis changes only the sign of y; reflection in the y-axis changes only x; a 180° rotation about the origin changes both signs.
Question 9out of 10
When a point is reflected in the y-axis, which coordinate changes sign?
Reflection in the y-axis preserves y and reverses the sign of x: (x, y) → (−x, y). The image is the same distance on the other side of the vertical axis.
Question 10out of 10
Point A(-5, 6) is rotated 180° about the origin. Find its new coordinates.
A 180° rotation about the origin reverses both coordinate signs: (x, y) → (−x, −y). The distance from the origin stays the same.
Time left: 00:00:00
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Sample questions
- Point A(___, ___) is translated by ___ units in the x-direction and ___ units in the y-direction. Find its new coordinates.
- Point A(___, ___) is reflected in the x-axis. Find the image coordinates.
- Point A(___, ___) is reflected in the y-axis. Find the image coordinates.
- Point A(___, ___) is rotated 180° about the origin. Find its new coordinates.
- Point A(___, ___) is translated twice by the same vector (___, ___). Find the final coordinates.
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.
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