Translation Rules
A triangle is moved 3 units right and 2 units up. What is this transformation called?
A translation
What is a dilation?
A transformation that changes the size of a figure.
What is the image of point A(3, 2) after a translation of (x + 1, y + 3)?
(4, 5)
True or False: Translations change the size of a shape.
False
Sean said, "After a translation, the new shape has bigger angles and longer sides.” Find and correct his mistake.
A translation does not change size or angles — the shape stays congruent.
If a shape is translated 5 units left, how does the x-coordinate of each point change? Think adding or subtracting from the x-coordinate.
It decreases by 5.
If a square with sides of 4 units is dilated by a scale factor of 2, what is the new side length?
8 units.
Point B is at (–1, 4). After a translation (x + 5, y - 2), where is B’?
(4, 2)
True or False: Dilations always produce congruent shapes.
False, (they’re similar, not congruent)
Shane said, "This triangle was dilated by a scale factor of 2, so it is the same size as the original.” Find and correct his mistake.
Dilation with a scale factor of 2 makes the triangle larger, not the same size.
What kind of transformation keeps the same size and shape, just moves the figure?
A translation
What does a scale factor of 1 do to a shape? Think about what happens when you multiply something by 1.
It keeps the shape the same size (no dilation).
Point C(6, –3) is dilated by a scale factor of 2. What are the coordinates of C’?
(12, –6)
True or False: A scale factor greater than 1 makes a shape larger.
True
Janet said, "Point A(2, 3) was translated using the rule (x - 1, y + 2), so the new point is (3, 5).” Find and correct her mistake.
The x-value should go down by 1, not up. The correct point is (1, 5).
A rectangle is translated 4 units right and 6 units down. What happens to the side lengths?
They stay exactly the same
If a triangle is dilated by a scale factor of 0.5, what happens to the size of the triangle?
It is half the size or the size is divided by 2.
Point D(–2, 8) is dilated by a scale factor of 0.5. What are the new coordinates?
(-1,4)
True or False: Dilation changes the angle measures of a shape.
False
Grace said, "I multiplied the coordinates (–2, 4) by 5 and got (–10, 20), so the shape is congruent.” Find and correct her mistake.
The shape is not congruent — it is the same shape but smaller. When size changes, shapes can no longer be congruent. Dilations change size.
Which of these transformations could be written as the rule (x + 2, y - 5)?
a) 2 units left, 5 units up
b) 2 units right, 5 units down
c) 5 units right, 2 units down
b) 2 units right, 5 units down
A shape is dilated using a scale factor of 3. One side was 2 cm. Which statement is true?
a) The new side is 1 cm
b) The new side is 6 cm
c) The new side is 3 cm
b) The new side is 6 cm
Point E(4, –6) is first translated by (x - 2, y + 4) and then dilated by a scale factor of 2. What are the final coordinates?
Start: (4, –6) →
Translate: (2, –2) →
Dilate: (4, –4)
True or False: A translation of 0 units in all directions leaves the shape unchanged.
True
John said, “A square with side lengths of 4 units is dilated by a scale factor of 3. The new side lengths are 7 units because 4 + 3 = 7.” Find and correct his mistake.
The student added instead of multiplying. Dilations require multiplying the side length by the scale factor. The correct side length is 4 × 3 = 12 units.