Autobots!
Define the following transformations:
-Translation
-Rotation
-Reflection
A translation is a geometric transformation that moves every point of a figure, shape or space by the same distance in a given direction.
A rotation is a motion of a certain space that preserves at least one point.
A reflection is a mirror image of a figure in the axis or plane of reflection.
What are the formulas for calculating slope?
y = mx + b
y = mx
Use substitution or elimination to solve the following system of linear equations:
4x - 12y = -8
-3x + 12y = 12
(4,2)
Explain what Pythagorean Theorem is.
Pythagorean's Theorem states that a right triangle the sum of the squares of the legs is equal to the square of the hypotenuse.
aka (a2+ b2 = c2)
Rewrite the expression using only positive exponents:
(7/16)-3
163 / 73
Define "rigid transformation"
A transformation where the size and shape of a figure does not change
When working with slope-intercept form, which variable represents the y-intercept?
b
Use substitution or elimination to solve the following system of linear equations:
6x - 9y = 18
-6x + 2y = 4
(0,2)
How do you know if 3 length measurements makes a triangle?
If the two smaller measurements when added together are bigger than the 3rd.
Write the following expression using only positive exponents:
19-3 x 19 x 19-4 x 193
1/193
What type of transformation keeps the figures' shape but not size?
Dilation
Solve the equation: 6(x+2) = 3(2x+4). How many solutions are there?
Infinitely many solutions
Use substitution or elimination to solve the following system of linear equations:
7x + 6y = 16
4x - 2y = 1
(1, 3/2)
A firefighter brings a 13-ft ladder to a burning building. He secures the ladder to the ground 5ft away from the wall. How high will the ladder reach?
12ft
Evaluate the expression:
34 x 3-6 x 90
1/9
Triangle PQR has the following vertices P(-4,4), Q(-2,3), and R(-5,2). The triangle is reflected across the x-axis and rotated 180 degrees clockwise. What are the coordinates of the vertices after the transformations?
P(4,4), Q(2,3) and R(5,2)
When you have the slope as both negative and a fraction, does the negative sign go to both the denominator and numerator, or only one of them?
Only 1; Numerator
Use substitution or elimination to solve the following system of linear equations:
x + y = 5
6x + 3y = 27
(4,1)
The perimeter of an equilateral triangle is 48cm. From the base to its height, how tall is the triangle? Round your answer to the nearest whole number.
The square root of 192 is between 13 and 14, but closer to 14.
Evaluate the expression:
( (3-4 x 36)/(63 x 6-1) )-2
16
Name 3 real-world applications of geometric transformations.
Examples include: engineering precision, architectural design, medical imaging analysis, computer graphics, robotics, automation, and navigation systems
Graph the following slope-intercept form:
y = -4x + 5
Your line in on the y-intercept at 5 and proceeds going down 4 and 1 to the right.
Use substitution or elimination to solve the following system of linear equations:
5x + 2y = 10
2x + y = 2
(6,-10)
Look at each set of three numbers and determine which are a Pythagorean triple?
2, 3, 4
4, 5, 6
5, 12, 13
6, 8, 10
8, 15, 17
9, 16, 25
5, 12 and 13
6, 8, and 10
8, 15 and 17
Evaluate the expression:
18-4 x 67
8/3