nd
2
9 weeks Review
Strategies for word problems
• Read the word problem- draw a picture if needed
• Circle all numbers (symbols, words, special words)
• Underline math vocabulary
• Box the question (?) or the commanding statement
• Equation – Write your equation
• Solve and look at all the answers.
Scatterplot Correlation (Association or Trend)
Positive linear correlation
• dots move along line to top
• As x increases, y also increases
Negative linear correlation
• Dots move along line to bottom
• As x increases, y decreases
Non-Linear correlation
• Dots move in a curve
No correlation
• Dots everywhere!
Your Turn
• What variables are
compared?
• What kind of
correlation is shown
• How many students
would you predict when
it is 13 years since
1999?
Systems of Equations
• Has 2 equations or 2 graphs.
• The solution is the point where both
graphs intersect.
• Make sure you identify the point
correctly. (X,Y)
• If you have to graph
• 1) make sure your equation is in y=mx+b
form
• 2) Make a table: x|equation|y|point
• 3) Plot your points
• 4)repeat for the other graph
• 5) Find the intersection (point that both
graphs share)
The solution
Is (-2,1)
Your turn
• Find the solution to the
systems shown.
Translations (Slides)
Looks Like
Effects:
• Translations preserve
both congruence and
orientation.
• Same shape & same size
Written translation:
The preimage was
translated 2 units right and
5 units down
Algebraic representation:
(x,y)(x+2, y-5)
Your turn
Write the algebraic representation
(x,y)(
Reflections (Flips)
Reflection across the x axis
• Reflection across the y axis
• Same size & shape
• Written description:
triangle ABC is reflected
across the x axis
• Algebraic Representation:
(x,y)(x, -y)
• Same size & shape
• Written description
• Quadrilateral KLMN is
reflected across the y axis
• Algebraic Representation
• (x,y)(-x,y)
Your turn
Algebraic Representation:
(X,Y)(
Rotations(Turns)- Rotated around a
point. Trace and turn like a clock.
360⁰ Rotation
Looks the same as
the original figure.
(x,y)(x,y)
Your Turn
Algebraic Representation:
(X,Y)(
Dilations – Enlargements & reductions
*The scale factor tells a lot. k which is called the scale 𝑓𝑎𝑐𝑡𝑜𝑟 =
Scale Factor < 1
Scale factor is less than 1
Scale Factor >1
Scale factor is greater than
1
𝑁𝑒𝑤 𝑚𝑒𝑎𝑠𝑢𝑟𝑒𝑚𝑒𝑛𝑡
𝑜𝑙𝑑 𝑚𝑒𝑎𝑠𝑢𝑟𝑒𝑚𝑒𝑛𝑡
Scale Factor = 1
Scale factor is equal to 1
Same Image!!!!
Congruent!!!!!
(x,y)(kx, ky)
(x,y)(½ x, ½ y)
(x,y)(kx, ky)
(x,y)(2x,2y)
(x,y)(kx,ky)
(x,y)(1x,1y)
Your Turn
Algebraic Representation:
(X,Y)(
Pythagorean Theorem
State the formula a2 + b2 = c2
How do you identify the hypotenuse?
a. The longest side
b. The opposite of the 90 degree
angle
3. How do you solve
a. Hypotenuse – you add
b. Leg – you subtract
4. It always has to be a right triangle and
don’t forget to look at the units!
1.
2.
*Key terms – diagonal, pictures in the shape
of a right triangle, length, distance between
points
Your Turn
Reading a model
How does this model
represent the Pythagorean
theorem?
Testing the converse
Real world problem
A triangle has sides with
lengths of 6 cm, 8cm, and
10 cm. Is it a right
triangle?
Mr. Harmon is leaning a
ladder against the side of
his house to repair the
roof. The top of the ladder
reaches the roof, which is
15 feet high. The base of
the ladder is 8 feet away
from the house, where Mr.
Harmon’s son is holding it
steady. How long is the
ladder?