4 units to the right

( x+4, y )

8 units down

( x, y  8 )

2 units left and 4 units up

( x  2 , y + 4 )

reflect over the y axis

(  x, y )

reflect over the x axis

( x,  y )

reflect over the line y=x

( y, x )

rotate 90 degrees cc

( y, x )

rotate 180 degrees cc

( x, y )

rotate 270 degrees cc

( y,  x )

A ( 2, 5), B (2, 4), C (3, 3)
Rotate AB 270 degrees cc

A' (5,2) B' (4,2)

A ( 2, 5), B (2, 4), C (3, 3)
Rotate BC 90 degrees clockwise

B' (4,2) C' (3,3)

A ( 2, 5), B (2, 4), C (3, 3)
Rotate ABC across the line y=x

A' (5, 2) B' (4, 2) C' (3,3)

A ( 2, 5), B (2, 4), C (3, 3)
Translate AC 3 units left and 2 units down

A' (5, 3) C' (0, 5)

A ( 2, 5), B (2, 4), C (3, 3)
Translate ABC 2 units right and 1 unit up, then dilate by a factor of 2

A' (0, 12) B' (8, 10) C' (10, 4)

A ( 2, 5), B (2, 4), C (3, 3)
Dilate AC by a factor of 3 then rotate 90 degrees clockwise

A' (15, 6) B' (9, 9)
(3y, 3x)

A ( 2, 5), B (2, 4), C (3, 3)
Translate AB up 2 units and down 2 units, then dilate by factor of 2, then rotate 270 degrees clockwise.

A' (4, 10) B' (4, 8)
A'' (10,4) B''(8, 4)

Describe
( x3, y+6 )

Translating 3 units left and 6 units up

If A' was rotated 270 degrees cc what were the original points of A?

A (2, 5)

parent function of linear equation

y = x

direct variation

y = kx

E (1, 3.5) F (4, 3) G (0, 1) H (4, 2)
Scale factor 0.5
Graph

E (1, 3.5) F (2, 1.5) G (0, 0.5) H (2, 1)

Classify
Angle 2 and 4

Corresponding Angles

Classify
Angles 5 and 10

Alternate Interior Angles

Classify
Angles 14 and 15

Same Side Interior Angles

Ana made a zip line for her tree house. To do this, she attached a pulley cable. She then strung the cable at an angle between the tree house and another tree. She made the drawing of the zip line at the left. The two trees are parallel. What is the measure of angle 1 and are angle 1 and the given angle sameside interior angles, alternate interior angles, or corresponding angles?

a) 105 degrees
b) Sameside interior angles

Identify all numbered angles that are congruent to the given angle

Angle 6: Vertical
Angle 4: Corresponding
Angle 2: Alternate Interior

Find angle 1 AND 2

Angle 1: 76 degrees ( alternate interior)
Angle 2: 180 degrees (same side interior)

Find the value of x. Then find the value of each labeled angle

x = 75
x+10 = 85
x+20 = 95
y = 110
y40 = 70

Find the values of the variables.

w = 59
x = 121
y = 59
v = 121
z = 53

Find the value of x.

x = 24

Simplify.
(n^4  2n 1) + (5n  n^4 + 5)

3n + 4

Simplify.
(2x^2  9x +11) (2x + 1)

4x^3  16x^2 + 11x + 11

(y^2  4w^2) ^2

y^4  8y^2 + 16w^4

The bisectors of the angles of a triangle intersect in a point that is equidistant from the three sides of the triangle

Incenter

The lines that contain the altitudes, intersect in a point

Orthocenter

The medians of a triangle intersect in a point that is twothirds the distance from each vertex to the midpoint of the opposite side

Centroid

The perpendicular bisectors of the sides of a triangle intersect in a point that is equidistant from the three vertices of the triangle. This construction is used to circumscribe a circle.

Circumcenter

A line that contains the midpoints of one side of a triangle and is parallel to another side passes through the midpoint of the third side

Midsegment

Midpoint formula

[( x1+x2) /2, (y1+y2)/2]

Midsegment = _____ of third side

1/2

3rd side = _____ midsegments

2

A segment from the vertex to the midpoint of the opposite side.

Median

The perpendicular segment from a vertex to the line that contains the opposite side

Altitude

The point of intersection of two or more lines

Point of concurrency

Median in ABC

CJ

Altitude for AHB

AH

Intersection of altitudes

Orthocenter

Name the orthocenter

Point Y

Pythagorean Theorem

c^2 = a^2 + b^2

Find x

3 *square root sign* 3

Find the value of y

8 *square root sign* 2

45  45  90 triangle

Hypotenuse = leg times square root of two

30  60  90 triangle

Hypotenuse = 2 times the short leg
Long leg = short leg times the square root of 3

(5 * the square root of 2)^2

5^2 * (the square root of 2)^2
25 * 2
50

Equation of a circle

r^2 = (xh)^2 + (yk)^2
Center: (h,k)

Tangent

opposite/adjacent

Sine

opposite/hypotenuse

Cosine

adjacent/opposite

SOH  CAH  TOA

SOH  CAH  TOA

Used when trying to find the measure of one of the acute angles, given the lengths of the side

Inverse Trigonometric Function

The length of the hypotenuse of a 30  60  90 triangle is 9. Find the perimeter.

27/2 + 9/2 * the square root of 3

______ ft = 1 mile

5280


2 miles


96

Distance formula

the square root of:
(x2  x1)^2 + (y2  y1)^2

To find the height of a pole, a surveyor moves 140 feet away from the base of the pole and then, with a transit 4 feet tall, measures the angle of elevation to the top of the pole to be 44 degrees. To the nearest foot, what is the height of the pole?

139 feet

Equation for finding discriminant

b^2  4ac

Discriminant
greater than 0: ___ solutions

2 solutions

Discriminant
equal to 0: ___ solutions

1 solution

Discriminant
less than 0: ___ solutions

no real number solutions
