Section 10.1 & 10.2: Distance & Midpoint Formulas, Equations of Cirlces

Pre­Calculus

March 14, 2016

Chapter 10: Conic SectionsConic Section - 2D shape that is created when you cut a double right cone with a plane.

A

B

Distance Formula

d = √(x2 ­ x1)2 + (y2 ­ y1)2

*based on the Pythagorean theorem   *c2 = a2 + b2, thus c = √a2 + b2

* a = (x2 ­ x1) and b = (y2 ­ y1)(x2, y2)

(x1, y1)

y2 ­ y1

x2 ­ x1

Section 10.1 & 10.2: Distance & Midpoint Formulas, Equations of Cirlces

Pre­Calculus

March 14, 2016

Find the distance between points.

1.) A(-3, 7) and B(2, -5)

2.) C(4, -2) and D(8, 3)

A

B

3. Find the midpoint of AB

Midpoint Formula

Midpoint = x2 + x1 , y2 + y1 2 2

*Midpoint is a point! Thus it must be written as an ordered pair!*Midpoint - exact middle

*average between two points*average the 2 x-values*average the 2 y-values

Section 10.1 & 10.2: Distance & Midpoint Formulas, Equations of Cirlces

Pre­Calculus

March 14, 2016

Find the midpoint of the segment that has endpoints at the two points given.

4.) A(-3, 7) and B(2, -5)

5.) C(4, -2) and D(8, 3)

10-2: Equation of a CircleDistance Formula:d = √(x2 - x1)2 + (y2 - y1)2

Standard Form Equation of a Circle(x - h)2 + (y - k)2 = r2k

-

(h, k) = center r = radius

(h, k)

(x, y)

circle - a set of all points a certain distance from a center point

Section 10.1 & 10.2: Distance & Midpoint Formulas, Equations of Cirlces

Pre­Calculus

March 14, 2016

Graph the circle.

6.) (x - 2)2 + (y+1)2 = 9 7.) x2 + (y - 6)2 = 7Center: Radius:

Center:Radius:360°

43

Write an equation for the circle described.

8.) Center (-5, 7), radius = 9 9. Center (2, 5) Point on circle: (4, 3)

Section 10.1 & 10.2: Distance & Midpoint Formulas, Equations of Cirlces

Pre­Calculus

March 14, 2016

Write an equation for the circle described.

10.) Endpoints of a diameter:(-3, 5) and (2, 9)

11.) Center (0, 4) Area = 17π

Write an equation for the circle described.

12.) Center (-2, 6) Circumference = 8π

13.) Center (0,0) Diameter = 2√6