Geometric Transformations
A triangle has vertices
A(2, 3), B(5, 7), and C(1, 4).
It is translated by the rule (x, y) → (x + 4, y − 2).
Find the coordinates of A', B', and C'
A→(6, 1)
B→(9, 5)
C →(5, 2)
A toy car's distance traveled after t seconds is given by
d(t) = 3t² + 2t.
Find the distance after t = 4 seconds
56 Units
A ball’s height is modeled by the quadratic function
h(t) = –2t² + 8t + 3
Find the height at t = 2 seconds.
11 Units
Two triangles are similar.
Triangle 1 has side lengths 3 cm, 4 cm, and 5 cm.
Triangle 2 is a scaled-up version where the shortest side is 9 cm.
What is the length of the longest side in Triangle 2?
15 cm
A bag contains 3 red, 5 blue, and 2 green marbles.
If one marble is chosen at random, what is the probability it is blue?
1/2
Reflect the point B(–4, 7) across the y-axis.
Find B'
B' = (4, 7)
A rectangle has length L = 3x + 5 and width W = 2x – 1
Write an expression for the perimeter.
10x + 8
A rocket is launched and its height is given by:
h(t) = –4t² + 12t + 5
What is the maximum height?
14 Units
In two similar triangles, the sides correspond as follows:
Triangle A side = 6
Triangle B matching side = 15
Another side of Triangle A is 8
Find the matching side in Triangle B
20 Units
You flip a fair coin and roll a standard 6-sided die.
What is the probability of getting heads and rolling a 6?
1/12
Point A(6, 2) is rotated 90° counterclockwise about the point (4, 2).
Find A'
A' = (4, 4)
A rectangular garden has area modeled by
A(x) = x² + 7x + 12.
Factor A(x) to find possible length and width.
Dimensions: (x + 3) and (x + 4)
A toy car’s position is modeled by:
p(t) = t² – 7t + 10
When does the car return to the starting height?
The car returns to the starting height at t = 2 sec and t = 5 sec
In a right triangle, the legs measure 8 and 15.
Find the length of the hypotenuse.
17 Units
A box has 4 black pens and 6 red pens.
Two pens are selected without replacement.
What is the probability both pens are black?
2/15
A quadrilateral has a vertex at Q(6, –4).
It undergoes the following transformations:
Reflect across the line x = 2
Rotate 180° about the origin
Translate left 7 units and up 1 unit
Find Q'.
Q' = (–5, 5)
A company models its revenue with
R(x) = x³ – 4x² – 21x.
Factor completely to find the values of x that make revenue 0
Revenue is 0 when x = 0, 7, –3
A ball is thrown upward and its height is given by:
h(t) = –5t² + 20t + 15
After how many seconds does the ball hit the ground?
Approximately 4.65 seconds
In a right triangle, an altitude is drawn from the right angle to the hypotenuse, creating two smaller right triangles.
If the whole hypotenuse measures 20, and one of the smaller hypotenuse segments is 5, find the altitude.
5√3 units
A teacher randomly chooses 3 students from a group of 10 to work on a project.
How many different groups of 3 can be made?
120 groups
A drone is located at point E(4, –3).
It performs the following movements:
Reflect across the y-axis
Rotate 180° about the origin
Translate 3 units up
Find the drone’s final position.
(4, 6)
A catapult launches a stone and its height is modeled by
h(t) = –5t² + 30t – 40.
When will it hit the ground?
The stone hits ground at t = 4 seconds.
A company’s profit from selling x items is modeled by:
P(x) = –3x² + 24x – 20
Find:
The number of items that gives maximum profit
4 Items
A ladder leans against a wall forming a 74° angle with the ground.
The bottom of the ladder is 6 feet away from the wall.
How long is the ladder?
Approximately 21.8 feet
In a school, 40% of students play a sport.
Of those who play a sport, 70% also participate in an after-school club.
What is the probability that a randomly selected student plays a sport AND is in a club?
28%