Transformations
(Robots in Disguise?)
(Robots in Disguise?)
Name the three types of rigid transformations
In the equation y=2x+3y=2x+3, identify the rate of change and the vertical intercept.
Rate of change: 2; Vertical intercept: 3
Solve: x+5=12
x = 7
What is a function?
A function is a relationship between inputs and outputs where each input has exactly one output
Evaluate
sqrt16
4
What do you call the point around which a figure rotates?
Center of rotation
Write the equation of a line that has a slope of 4 and a vertical intercept of -2.
y=4x−2y=4x−2
Determine whether x=3 is a solution to 2x−1=5
Yes, 2(3)−1=5 is true
If the input to a function is 2 and the output is 7, write an ordered pair that represents this.
(2,7)
Is sqrt2 rational or irrational
Irrational
If a line segment is 5 cm long and undergoes a rigid transformation, what will be the length of the transformed segment?
5 cm (rigid transformations preserve distance)
What is the relationship between a proportional relationship and a linear relationship?
A proportional relationship is a special case of a linear relationship where the vertical intercept is 0
Solve: 2x+3=11
x = 4
Explain the difference between an independent variable and a dependent variable.
An independent variable is the input (what you control); a dependent variable is the output (what depends on the input)
State the Pythagorean Theorem.
In a right triangle, a^2+b^2=c^2 , where a and b are the legs and c is the hypotenuse
Define what it means for two figures to be congruent.
Two figures are congruent if one can be obtained from the other by a sequence of rigid transformations
A line passes through (0, 5) and (2, 9). Write the equation of the line.
y=2x+5y=2x+5
A system of two linear equations has no solution. What does this tell you about the graphs of the two lines?
The two lines are parallel (they have the same slope but different y-intercepts)
SUPRISE VOLUME QUESTION
Use the formula V= pir^2h to find the volume of a cylinder with radius 3 cm and height 5 cm.
141.3 cubic cm
A right triangle has legs of length 3 and 4. What is the length of the hypotenuse?
c = 5
A triangle has angles measuring 60°, 70°, and 50°. After a rotation of 180°, what are the angle measures of the rotated triangle?
60°, 70°, and 50° (angles are preserved under rotation)
If a situation is represented by the equation y=3x+20y=3x+20, interpret what the 3 and the 20 mean in the context of the situation.
The 3 represents the rate of change (for each unit increase in x, y increases by 3); the 20 represents the starting value or initial amount
Solve the system: y=2x+1 and y=−x+4
(1,3)
SURPRISE EXPONENT QUESTION
Simplify: 10^5 x 10^2
10^7
Approximate sqrt50 to the nearest tenth by identifying which two consecutive whole numbers it falls between.
approximately 7.1