Grade 8 Mathematics
A TRANSFORMATION changes the position, size, or orientation of a figure.
Rigid transformations (translations, reflections, rotations) keep figures CONGRUENT
Dilations create SIMILAR figures (same shape, different size)
Moves every point the same distance and direction
Preserves size and shape
Flips figure over a line (mirror image)
Preserves size and shape
Turns figure around a center point
Preserves size and shape
Enlarges or shrinks by a scale factor
Changes size, keeps shape
Translate point A(3, 2) by 4 units left and 3 units up
Write the rule: (x, y) → (x - 4, y + 3). Left means subtract from x, up means add to y.
Apply to point A: A(3, 2) → A'(3 - 4, 2 + 3) = A'(-1, 5)
Reflect point B(4, -2) over the x-axis, then over the y-axis
Over x-axis: Change sign of y. B(4, -2) → B'(4, 2)
Over y-axis: Change sign of x. B'(4, 2) → B''(-4, 2)
Notice: Reflecting over BOTH axes is the same as rotating 180 degrees!
Rotate point C(3, 1) 90° counterclockwise about the origin
Use the rule: (x, y) → (-y, x)
Apply: C(3, 1) → C'(-1, 3)
Tip: The new x is the OPPOSITE of the old y. The new y is the old x.
Dilate point D(2, -4) with scale factor k = 3, center at origin
Use the rule: (x, y) → (kx, ky) = (3x, 3y)
Apply: D(2, -4) → D'(6, -12)
Scale factor > 1 = enlargement | Scale factor < 1 = reduction
WRONG: "All transformations create congruent figures."
RIGHT: Only RIGID transformations (translation, reflection, rotation) create congruent figures. Dilations create SIMILAR figures (same shape, different size). Congruent = same size AND shape. Similar = same shape, proportional sizes.
1. Translate point P(5, -3) by 2 units right and 4 units down.
P' = (, )
2. Reflect point Q(-2, 6) over the y-axis.
Q' = (, )
3. Rotate point R(4, -2) 90° counterclockwise about the origin.
R' = (, )
4. Dilate point S(-3, 6) with scale factor 2, center at origin.
S' = (, )
5. A triangle is translated, then reflected. Are the original and final images congruent or similar?
Answer: