5.7 Use Figures in Three – Dimensional Space

Pg. 205

Topics Covered

• Plotting in the 3 –D System– Rectangular Prism– Point

• Use of the Distance and Midpoint Formula in the 3 – D System– Between two points in the 3 – D system

• Today we will Recognize and Graph the Equation of a Plane and Write the Equation for a Sphere

TODAY

Recognize and Graph the Equation of a Plane

• Graph the Equation3x + 2y + 4z = 12

– In order to solve we will use the intercept method. Once we have the intercepts of each axis, we then plot the points on the three axes and connect the “three” dots.

– It is a Triangle

3x + 2y + 4z = 12

• Intercept Method

+y

+x

+z

Plot and connect the points

Write the Equation for a Sphere

• Just as we expanded the equations for Midpoint and Distance, we can do this for the equation for a sphere.– A sphere is a 3 – D circle, So what is the equation of a

circle?

– We will expand using the “z” variable.

– But now we may have to use “Complete the Square” on three variables…………….

220

20 ryyxx

220

20

20 rzzyyxx

HA HA HA HA HA

Write the Equation of a Sphere in Standard Form with center (1, 5, -3) and radius = 5

• Standard Form

• x0, y0, z0, are (1, 5, -3)

220

20

20 rzzyyxx

01862222 zyxzyx

Homework

Correct Worksheet #1

Due Monday