Other Concepts

Question 1

For an “overlapping sets” problem with three overlapping compenents requiring three circles…

The TOTAL

=

Answer 1

(A+B+C) - (Σ Doubles) - 2(Σ Triples) + N

or

(Component_A + Component_B + Component_C) - (Sum of the Doubled Compenents) - 2(Sum of Tripled Components) + Neither category

Question 2

y = mx + b

what does each letter represent?

Answer 2

Question 3

Slope of Perpendicular Bisector Line

Answer 3

= Negative reciprocal of the original line

Original Line Slope = 1/2

Perpendicular bisector line = -2

Question 4

Given: Initial Coordinate (a,b)

What else do you need to define a line?

Answer 4

One of the following…

1. The slope of the line, or the slope of a line perpendicular or parallel to the line
2. Another point on the line (x intercept, y intercept, or any other point)

Question 5

Y Intercept

Answer 5

Where the line in question crossed the Y axis

X must equal “0”

Point must be in this form: ( 0,Y )

Question 6

X Intercept

Answer 6

Where the line in question crossed the X axis

Y must equal “0”

Point must be in this form: ( X,0 )

Question 7

Parallel Lines

Answer 7

Same slope

Different y-intercepts

Question 8

Line Reflection over the X-axis

( x,y )

becomes…

Answer 8

( x,-y )

Question 9

Line Reflection over the Y-Axis

( x,y )

becomes

Answer 9

( -x,y )

Question 10

Reflection over the Origin

(Point Reflection)

( x,y )

becomes

Answer 10

( -x,-y )

Question 11

Reflecting a Polygon

Answer 11

Reflect vertices as directed

over the x-axis, y-axis, or origin

connect the dots = newly reflected polygon!

Question 12

Y = X Line Reflection

( x, y )

becomes

Answer 12

( y, x )

Question 13

Y = -X Line Reflection

( x,y )

becomes

Answer 13

( -y, -x)

Question 14

Distance )( two points

=

Answer 14

Question 15

Same y-coordinates

Point A = ( 3,2 )

Point B = (-5,2 )

then the distance )( the two points

=

Answer 15

The absolute value of the difference between the x coordinates

Distance = 2

3-5 |

Question 16

Same x-coordinates

Point A = ( 4,5 )

Point B = ( 4,2 )

then the distance )( the two points

=

Answer 16

The absolute value of the difference between the y coordinates

Distance = 3

5-2 |

Question 17

Calculating the Mid-Point )( two points

Answer 17

Question 18

Reflection over point ( a,b )

When point ( x,y ) is reflected over point ( a,b )

Answer 18

the new ( x,y ) ⇒ ( 2a-x, 2b-y )

Question 19

Reflection over line x = a

• When a point ( a,b ) is reflected over the line x = a *
• *a = #*

Answer 19

( x,y ) ⇒ ( 2a-x,y )

Question 20

Reflection over line y = b

• When a point ( a,b ) is reflected over the line y = b *
• *b = #*

Answer 20

( x,y ) ⇒ ( x, 2b-y )