Module 7: Connecting Algebra and Geometry by Elora Dannan

New Vocabulary

dannane9085 — 2017-03-21 01:14:18 UTC

Vector - a quantity having direction as well as magnitude, especially as determining the position of one point in space relative to another.
 Magnitude - the great size or extent of something.
Scalar multiplication- one of the basic operations defining a vector space in linear algebra (or more generally, a module in abstract algebra).
 Directed line segment- is a portion of a line that has both a magnitude and direction.
 Resultant vector- The combination of two or more single vectors. When used alone, the term vector refers to a graphical representation of the magnitude and direction of a physical entity like force, velocity, or acceleration.

New concepts

dannane9085 — 2017-03-21 01:22:17 UTC

 Use coordinates to find distances and determine the perimeter of geometric shapes
 Prove slope criteria for parallel and perpendicular lines
 Use coordinates to algebraically prove geometric theorems
 Write the equation f(t)= m(t)+ by comparing parallel lines and finding k
 Determine the transformation from one function to another
 Translate linear and exponential functions using multiple representations
 Defining and operating with vectors as quantities with magnitude and direction
 Properties of matrix addition and multiplication, including identity and inverse properties
 Finding the determinant of a matrix and relating it to the area of a parallelogram
 Solving a system of linear equations using the multiplicative inverse matrix
 Using matrix multiplication to reflect and rotate vectors and images
 Solving problems involving quantities that can be represented by vectors

Helpful video

dannane9085 — 2017-03-21 01:24:44 UTC

Another Helpful Video

dannane9085 — 2017-03-21 01:27:56 UTC

Example problem

dannane9085 — 2017-03-21 01:30:02 UTC

Add vectors V and W.
v= <1,5>, w= <4,6>
1+4=5
5+6=11
V+W= <5,11>

New Formulas

dannane9085 — 2017-03-21 01:40:49 UTC

f(x)=g(x)+k - shift up
f(x)=g(x)-k - Shift down
f(x)=g(x+k) - shift left
f(x)=g(x-k) - shift right
f(x)=-g(x) - Reflection across x-axis
f(x)=g(-x) - reflection across y-axis
f(x)=kg(x)- stretch vertically
f(x)=g(kx) - shrink horizontally
To get the determinate: 1/ad-cb (when using a matrix)
Inverted Matrix: [d -b]
[-c a]
Switch a and d, and make b and c negative ^^^