Polynomial Power
The area of a square is represented by x2+10x+25. What is the side length?
x+5
What transformation slides a figure without turning or flipping it?
Translation
How many lines of symmetry does a regular pentagon have?
5
Reflect (4, -2) across the x-axis.
Answer: (4, 2)
Find the midpoint of (2,8) and (6,4).
Answer: (4,6)
Simplify: (3x2+4x)+(2x2-7x)
5x2-3x
What transformation creates a mirror image across a line?
Reflection
If two figures have the same shape and size, they are called ______.
Congruent
Reflect (-5, 3) across the y-axis.
Answer: (5, 3)
Find the slope of the line through (1,2) and (5,10).
Answer: 2
Find the area of a rectangle with length (x+4) and width (x+2)
x2+6x+8
What transformation turns a figure around a fixed point?
Rotation
A regular octagon is rotated about its center.
What is the smallest angle of rotation that will map the octagon onto itself? Explain how you know.
Answer : 45°
Justification: A regular octagon has 8 equal sides. A full rotation is 360°.
360°÷8=45
Therefore, the smallest angle of rotational symmetry is 45°.
Point P(4, -2) undergoes a sequence of rigid motions:
Determine the final coordinates of the image and explain whether the image is congruent to the original figure.
Answer:(2,-4)
Rotation:
Reflection:
✅ Final coordinates: (2, -4)
✅ The image is congruent to the original because rotations and reflections are rigid motions that preserve distance and angle measures.
1 What is the distance between (0,0) and (0,8)?
2 The diagonals of quadrilateral ABCD have endpoints:
AC: A(0,0), C(8,6)
BD: B(2,6), D(6,0)
Use the midpoint formula to determine whether ABCD is a parallelogram.
1 Answer = 8
2 Midpoint:(x1+x2 , y1+y2)/2
Midpoint of AC:
((0+8)/2, (0+6)/2) = (4,3)
Midpoint of BD:
((2+6)/2, (6+0)/2) = (4,3)
Since the diagonals bisect each other:
✅ ABCD is a parallelogram
The area of a rectangle is represented by x2+9x+20. One side length is x+5. Determine the other side length and justify your answer.
x+4
A transformation maps point A(2,3) to A'(2,-3). Describe the transformation and explain how you know.
Reflection over the x-axis.
The x-coordinate stays the same while the y-coordinate changes sign.
A regular hexagon has rotational symmetry.
What is the smallest angle of rotation that maps the hexagon onto itself?
360° ÷ 6 = 60°
Triangle ABC is translated 5 units right and 2 units down.
If A(1,4), B(3,6), and C(5,2), determine the coordinates of A', B', and C'.
Answer:
A'(6,2)
B'(8,4)
C'(10,0)
The vertices of a quadrilateral are
A(0,0), B(4,2), C(6,6), D(2,4)
Use slopes to classify the quadrilateral.
Answer:
AB = 2/4 = 1/2
CD = 2/4 = 1/2
BC = 4/2 = 2
DA = 4/2 = 2
Opposite sides are parallel.
Classification: Parallelogram
A rectangular patio has dimensions (2x+3) and (x−2). Write and simplify a polynomial representing the area. Then determine the area when x=6.
Area = (2x+3)(x-2) = 2x2 - x - 6
When x=6
=2(6)2 - (6) - 6
=60 sq units
Area = 60 sq units
Point P(-4,2) is reflected across the y-axis and then translated 3 units down.
What are the coordinates of the final image?
Reflection:
(-4,2) → (4,2)
Translation:
(4,2) → (4,-1)
Final answer: (4,-1)
A figure is reflected across a line and then translated.
Can the resulting figure be congruent to the original? Explain why or why not.
Yes.
Reflections and translations are rigid motions that preserve side lengths and angle measures. Therefore the image remains congruent to the original.
Point M(2,-1) is rotated 180° about the origin and then reflected across the x-axis.
Determine the final coordinates.
Answer:(-2,-1)
180° Rotation:
(2,-1) → (-2,1)
Reflection over x-axis:
(-2,1) → (-2,-1)
Final answer: (-2,-1)
Vertices:
A(0,0), B(4,0), C(4,4), D(0,4)
Use distance and slope to determine the most specific classification.
Answer: Square
✅ Square