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Geometry Transformations Practice
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Geometry Transformations Practice
A design studio is testing transformations for a repeating logo. Use the coordinate rules and points given in each question. For coordinate pairs, write the image of each point as (x, y). A prime (′) labels an image point.
Spot and describe transformations
1.A logo moves without turning or flipping: every point shifts 4 units left and 2 units up. Name the transformation and give its translation vector in (horizontal, vertical) form.
2.A motif is reflected in the line y = x. Which rule maps any point (x, y) to its image?
- (x, −y)
- (−x, y)
- (y, x)
- (−y, −x)
3.A triangular logo has vertices A(1, 2), B(4, 2) and C(2, 5). It is translated by vector (−3, 1). Find A′, B′ and C′.
4.The points P(−2, 3), Q(1, 4) and R(3, −1) are reflected in the y-axis. Complete the table with each image coordinate.
Original point
Reflected image
P(−2, 3)
P′ =
Q(1, 4)
Q′ =
R(3, −1)
R′ =
5.A point (x, y) is rotated 90° anticlockwise about the origin. Choose the rule for its image.
- (y, −x)
- (−y, x)
- (−x, −y)
- (x, −y)
Test the design rules
6.Rotate triangle A(2, 1), B(5, 1), C(3, 4) by 90° clockwise about the origin. Give the coordinates of A′, B′ and C′.
7.A point (6, −2) is reflected in the x-axis, then translated by vector (−1, 3). Find its final coordinates. Show the intermediate reflected point too.
8.True or false? A reflection preserves side lengths and angles, but reverses orientation. Give one sentence to justify your answer.
TrueFalse
9.A logo point moves from M(−3, 2) to M′(2, 2). Describe the translation using a vector, and state how far and in which direction it moves.
10.A point (4, −1) is reflected in the line y = x and then reflected in the y-axis. Find its final coordinates. What single transformation has the same effect?
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