Unit 1 Review
What are we doing to the variable when we are solving equations?
Isolating the variable
Getting the variable to be alone
What does the word congruent mean?
A transformation that does not change the size or shape of a geometric object is known as what?
What is true about all similar figures sides and angles?
Similar figures have corresponding sides that are proportional and corresponding angles that are congruent.
What does the m and b represent in the equation y=mx+b?
m = slope (change in y/change in x)
b = y-intercept
How many terms does the following expression have?
2x + y - 8
Bonus: +100 pts.
What is the name of an expression with that many terms?
3 terms
bonus: Trinomial
What is a midpoint of a segment?
The midpoint is the exact middle point. It is a point halfway between both end points.
What is the rule for when you reflect over the x-axis?
The y-value flips signs
* count number of units until you hit the x axis and then keep going that number of units past the axis *
If you are dilating A(4,6) with a scale factor of 1/2 and the center is at the origin, how can you find where the image of A will lie?
Multiply all numbers in the coordinate by 2.
A(4, 6) --> A'(4(1/2), 6(1/2)) --> A' (2, 3)
For the line y= - 1/4 x - 3, what would be an incorrect representation of the slope?
a. - 2/8
b. 20/-80
c. - 4 / -16
d. - 3 / 12
A negative divided by a negative is a positive.
-8 -8
1/2 x = 16
(2/1) (1/2) x = 16 (2/1)
x = 32
Equal or Supplementary?
Alternate Interior/Exterior Angles
Same Side Interior/Exterior Angles
Corresponding Angles
Alternate Interior/Exterior Angles - Equal
Same Side Interior/Exterior Angles - Supplementary
Corresponding Angles - Equal
What do you do when you rotate a point by 90/180/270 degrees clockwise/counter clockwise?
- counter clockwise means to turn your paper to the left
- 90 degrees means to turn the paper one time
- 180 degrees means to turn the paper two times (upside down)
- 270 degrees means to turn the paper three times
A dilation changes the size of a shape. This makes figures similar, not congruent.
The steepest slope is the slope with the highest number.
What is an inconsistent equation? How many solutions does it have?
Identity: Equations that are the exact same. It does not matter what you plug in for the variable, they will always be equal
Ex: 3x + 6 = 3x + 6
Inconsistent: Equations that do not have a solution.
No matter what, 6 will never equal 4. Therefore, no matter the variable, the two will never be equal.
Ex: 3x + 6 = 3x + 4
Two lines are parallel and intersect transversal p.
Corresponding angles are <A and <B. Find the measure of x.
m<A = 12x-38
m<B = 4x-6
Same side interior = Supplementary
12x-38=4x-6
-4x -4x
8x - 38 = -6+ 38 + 38
8x = 32
/8 / 8
x = 4
A transformation is given by the rule
(x, y) -> (x + 3, y - 8).
Which of the following describes the effect of this transformation on an object?
This means you would move the point 3 units to the right, and then go down by 8 units.
OR you can add 3 to the x value and subtract 8 from the y value
In the diagram below, triangle ABC and triangle DEF are similar. Which of the following is the length of side DF? The following lengths are given:
AB = 12, AC = 16 and DE = 18. Find the length of DF.
AB/AC = DE/DF
12 / 16 = 18 / x
3 / 4 = 18 / x
3(6) = 18
4(6) = 24
x = 24
What is the slope between the two points (5,8) and (1,0)?
m = y2-y1 / x2-x1
m = 0-8 / 1-5
m = -8/-4
m = 2
Solve for x:
3(x-2)+4 = 3x+6
3(x-2)+4 = 3x+6
3x - 6 + 4 = 3x + 6
3x - 2 = 3x + 6
-3x -3x
-2 = 6 <-- This is not true
Therefore, the system has 0 solutions
* Think about what supplementary means!!
4x + 36 = 180
-36 -36
4x = 144
/4 /4
x = 36
A translation maps the point A(-4, 7) to the point A'(6, 11). What is the image of the point B(4, 15) after the same translation?
There are 10 units between -4 and 6 meaning they added 10 to the x value. There are 4 units between 7 and 11 meaning they added 4 to the y value.
Therefore, 4+10 = 14 and 15+4 = 19 so
B' ( 14, 19 )
Triangle with points A (2,4), B (2,2), C (6,2)
are mapped to A' (4, -8), B' (4,-4), C' (12,-4)
What is a sequence of transformations that could be used to map triangle ABC onto triangle A'B'C'?
A dilation with the center at the origin and a scale factor of 2. This would result in (4,8), (4,4), (12,4). In order to get the image points, we would need to do a reflection over the x-axis creating the new points A'(4,-8), B'(4,4) and C'(12,-4).
Solve the following system of equations algebraically:
y= - x + 4 and y= - 4x - 2
Set them equal to each other!
-x + 4 = - 4x - 2
+4x +4x
3x + 4 = -2
-4 -4
3x = -6
/ 3 /3
x = -2
y= -(-2) + 4 = 2+4 = 6
y = - 4 (-2) -2 = 8-2 = 6
Solution: (-2, 6)