Tolentino Reviewer

Scientific Calculator Techniques in Plane and Analytic Geometry By Engineer Romeo Q. Tolentino Professor National University

A complex number as a vector • A complex number A = x + yi can be modeled as a vector with magnitude |A| and angle with respect to the positive x axis as arg(A). • Example: If A = 3 + 4i , find the magnitude of A and its absolute value. • STEP 1: ENTER: MODE 2 • STEP 2: Input | A | CALC SHIFT hyp Alpha (-) CALC 3 + 4 ENG • Display: • A? • 3 + 4i • Step 3: ENTER: = • Output: |A| • 5 •   • To get the argument: • STEP 4: Input Arg(A) = SHIFT 2 1 Alph (-) ) • Display: • arg(A) • 53.13010235

Diagram of Vector A

Complex Number as Coordinates (x,y) A complex number A = x + yi can be modeled as coordinates ( x, y). Examples: The coordinates ( 3, 5) can be written as 3 + 5i. The coordinates ( -6, 7) can be written as -6 + 7i.

Distance between 2 points Since A and B can be modeled as 2 two coordinates ( x1, y1) and ( x2, y2) and at the same time vectors A and B with initial points emanate from the origin , then the distance between 2 points A (x1, y1) and B( x2, y2) is the length of the difference vector of A – B. d = |A- B|.

Example for Distance between 2 points

THE COSINE LAW CAL TECH

  Distance between 2 points in 3 Dimension

Division of Line Segment

Distance between a point and a line

Distance between a point and a line Example

  Modeling a straight line

A line can be modeled by curve fitting. If two points are fitted in the linear regression model, then we have a perfect line.

Example of using the Line Model

LOCATING THE VERTEX OF THE PARABOLA y = AX2 + BX + C

The highest or lowest point of the parabola can be determined by maximizing ( minimizing y using CALCULUS )  y = AX2 + BX + C dy/dx = 2AX + B = 0 X = - B/(2A) (This is the abscissa of the vertex. ) Then the value of y can be found by substituting X = -B/(2A) to the equation of the parabola.

Example for Locating Vertex of the parabola

Modeling a Parabola

Modeling a Circle using Regression

Example (Modeling a Circle)

Finding Area of a Segment of a Circle

Modeling the Arithmetic Progression

Coordinate Transformation

REMOVAL OF THE XY TERM in the General Conics Ax2 + Bxy + Cy2 + Dx + Ey + F = 0