Geometry Regents Formulas

Question 1

Midpoint Formula

Answer 1

(x¹ + x²)/2, (y¹ + y²)/2.

Question 2

Point-Slope Formula

Answer 2

y-y₁=m(x-x₁)

Question 3

Distance Formula

Answer 3

√(x₂ - x₁) ² + (y₂ - y₁)²

Question 4

Slope Formula

Answer 4

y₂ - y₁/x₂ - x₁

Question 5

Pythagorean Converse: a²+b²=c²

Answer 5

Right Triangle

Question 6

Pythagorean Converse: a²+ b² > c²

Answer 6

Acute Triangle

Question 7

Pythagorean Converse: a²+ b² < c²

Answer 7

Obtuse Triangle

Question 8

sin

Answer 8

opposite/hypotenuse

Question 9

cos

Answer 9

adjacent/hypotenuse

Question 10

tan

Answer 10

opposite/adjacent

Question 11

Opposite

Answer 11

What the angle is facing

Question 12

Adjacent

Answer 12

Next to the angle put not the hypotenuse

Question 13

Hypotenuse

Answer 13

Doesn’t form a perpendicular angle

Question 14

Elevation

Answer 14

If the triangle is going up

Question 15

Depression

Answer 15

If the triangle is going down

Question 16

Slope Intercept Formula

Answer 16

y=mx+b

Question 17

Same Side Interior Angles

Answer 17

Are supplementary angles, are congruent, and on the same side

Question 18

Average Speed

Answer 18

Distance/Time

Question 19

What is the Pythagorean Theorem used for?

Answer 19

To find a missing right triangle side length

Question 20

Reflection over the x axis

Answer 20

(x,y) -> (x,-y)

Question 21

Reflection over the y axis

Answer 21

(x,y) -> (-x,y)

Question 22

Reflection y=x

Answer 22

(x,y) -> (y,x) (goes diagonally to the right)

Question 23

Reflection y=-x

Answer 23

(x,y) -> (-y, -x) (goes diagonally to the left)

Question 24

Rotation 90 Degrees Counterclockwise or 270 degrees clockwise

Answer 24

(x,y) -> (-y, x)

Question 25

Rotation 180 Degrees Counterclockwise or 180 degrees clockwise

Answer 25

(x,y) -> (-x, -y)

Question 26

Rotation 270 Degrees Counterclockwise or 90 degrees clockwise

Answer 26

(x,y) -> (y,-x)

Question 27

What way do you work with transformation when you see a ° symbol

Answer 27

Work the transformations from right to left

Question 28

General/Standard Equation of a Circle:

Answer 28

x² + y² + Cx + Dy + E = 0

Question 29

Center – Radius Equation of a Circle:

Answer 29

(x-h)²+(y-k)²=r²

Question 30

Central Angle:

Answer 30

A piece from the center of a circle the arc and angle with be in the same degrees

Question 31

Inscribed Angle:

Answer 31

An angle from the end of a triangle, the angle will be half of the arc’s angle

Question 32

Tangent-Chord Angle:

Answer 32

has a line inside the circle and outside of the circle ∠x =(1/2) arc AB

Question 33

If the angle is outside of the circle but forms in the circle

Answer 33

(big arc - little arc)/2 = ∠x

Question 34

Two Cord Angle

Answer 34

Angle inside a circle when to lines inside the circle bisect
Formula: Arc¹ + Arc²/2

Question 35

Mass

Answer 35

Density times Volume

Question 36

Density

Answer 36

Mass/Volume

Question 37

Cross Section

Answer 37

A shape making a cut into another shape

Question 38

What is a quadrilateral

Answer 38

A four shaped shape

Question 39

Trapezoid

Answer 39

At least one pair of parallel sides

Question 40

Consecutive Angles

Answer 40

Angles on the same line that add up to 180 degrees

Question 41

Median

Answer 41

A line from the vertex to the midpoint

Question 42

Circumference Formula

Answer 42

2πr

Question 43

Circumference

Answer 43

Distance Around A Circle

Question 44

Arc Formula

Answer 44

πrθ/180

Question 45

Secant

Answer 45

a line that intersects a circle at two points

Question 46

Tangent

Answer 46

is a line that intersects a circle at on point

Question 47

Sector

Answer 47

A portion of a circle

Question 48

How to find the area of a sector

Answer 48

(θ/360)πr²

Question 49

How to find a point on a line when they give a ratio of the segments

Answer 49

x₁+(a/a+b)(x₂-x₁)
–> For X Coordinate
y₁+(a/a+b)(y-y₁))
–> For Y Coordinate
Combine the X and Y to get the point on a line

Question 50

When do you use point slope formula

Answer 50

When you only have one point that you need to find the slope and y intercept of.