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Point A(3, −2) is translated 5 units left and 4 units up. What are the coordinates of A′?
A'(-2,2)
Reflect A(4, −3) over the x-axis. Find A′.
A′(4, 3)
Rotate A(2, 5) 90° counterclockwise about the origin. Find A′.
A′(−5, 2)
A(−2, 4) → A′(−2, −4). What transformation occurred?
Reflection over the x-axis
Which transformations always preserve side lengths and angle measures: translations, reflections, rotations, or all three?
All three
Write the rule for a translation 6 units right and 3 units down.
(x, y) → (x + 6, y − 3)
Write the rule for a reflection over the y-axis.
(x, y) → (−x, y)
Write the rule for a 180° rotation about the origin.
(x, y) → (−x, −y)
A(3, −1) → A′(−3, 1). What transformation occurred?
180° rotation about the origin
A rule is (x,y) → (x−4,y+7). Name the transformation and describe it.
Translation 4 left and 7 up
Triangle ABC has A(−4, 2), B(−1, 2), C(−3, 5). Translate it 3 right and 4 down. Give A′, B′, C′.
A′(−1,−2), B′(2,−2), C′(0,1)
Triangle ABC has A(2, 5), B(6, 5), C(4, 1). Reflect over the y-axis. Give the image coordinates.
A′(−2,5), B′(−6,5), C′(−4,1)
Rotate B(−3, 6) 90° clockwise about the origin. Find B′.
B′(6, 3)
A(−5, 2) → A′(1, 2). What transformation occurred?
Translation 6 units right
A point (a,b) is reflected over the y-axis and then translated 3 right. Write the final coordinates in terms of a and b.
(3−a, b)
A point moves from (−7, 4) to (2, −1). What translation rule maps the original point to its image?
(x,y) → (x + 9, y − 5)
A′(−8, 3) is the reflection of A across the x-axis. What is A?
A(−8, −3)
Triangle ABC has A(1,−2), B(4,−2), C(2,−5). Rotate 270° counterclockwise about the origin. Give the image coordinates.
A′(−2,−1), B′(−2,−4), C′(−5,−2)
A(2, 7) → A′(−7, 2). What transformation occurred?
90° counterclockwise rotation about the origin
OR
270° clockwise rotation about the origin
A(2,−3) is rotated 90° counterclockwise, then reflected over the x-axis. What is the final point?
(−3,−2)