3-d Distance, Midpoint, and Intercepts

3-d TEST THURSDAY!!!

Midterm: Oct. 8

Finding the distance between 2 points

2122

122

12 zzyyxxd 2122

12 yyxxd

2D (x, y)3D (x, y, z)

Finding the distance between 2 points in 3-dimentional space

(3, -2, 5)

(-1, 4, -2)

2122

122

12 zzyyxxd

Find the distance between the 2 points

1. (10, 2, –3 ) and (6, 4, –5)

2. (–1, 3, 4) and (0, –5, 2)

Finding the midpoint of the 2 points

2,

22121 yyxx

MP

2D (x, y)3D (x, y, z)

2,

2,

2212121 zzyyxx

MP

Find the midpoint of the 2 points

1. (10, 2, –3 ) and (6, 4, –5)

2. (–1, 3, 4) and (0, –5, 2)

Graph the equation of the plane3x + 2y + 4z =12

Find the x, y and z intercepts by plugging in 0’s.

X

Z

Y

Equations of Spheres

TEST THURSDAY!

Midterm: Oct. 8

Standard form for a sphere

2 2 2 2x h y k z l R

Where (h, k, l) is the center of the sphere and R is the radius of the sphere

Give the center and the radius of each sphere.

2 2 2

2 22 2

2 2 2

1. 3 2 1 49

2. 1 1 4

3. 31

x y z

x y z

x y z

Center (3, -2, -1) Radius 7

Center (1, 0, 1) Radius 4

Center (0, 0, 0) Radius 31

Page 206 – Guided Practice #4

Write an equation of a sphere in standard form with center (4, -2, 0)

and radius 7

(x -4)2 + (y + 2)2 + z2 = 49

Give the center and the radius of each sphere.

2 2 24. 4 6 8 4x y z x y z

2 2 22 3 4 25

(2, 3,4) 5

x y z

Center Radius

Surface Area and Volume of a Sphere

• Surface Area

• Volume

24 rA

3

3

4rV

Homework

• Page 207 #1-19odds– Odds so you can check your answers…

• Page 208 #15, 16

• Worksheet – Turning in for a grade!