3-Dimensional Coordinate System

3-Dimensional Coordinate System

Building Off Our Notes from Tuesday

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Review from Yesterday

• When plotting a point in space, we need a 3rd Axis, the z-axis

• Because of this, any point in space would have the coordinate of (x,y,z) ALWAYS IN THIS ORDER!!

• We can use the same midpoint and distance formulas from Algebra for these 3D points, just with the z-portion added on

Midpoint Formula for 3D Coordinates

Add the x's, divide by two, repeat for the y's and z's. Your result is a coordinate in the 3D space.

Multiple Choice

What would be the midpoint between (0, 2, -5) and (3, 4, -2)?

• (3/2, 2, 3/2)

• (3/2, 3, -7/2)

• (-3/2, -3, -3/2)

Multiple Choice

What would be the midpoint between (10, -2, 7) and (4, 6, 15)?

• (11, 2, 7)

• (7, 2, 11)

• (3, 4, 4)

Distance Formula for 3D Coordinates

Same as old Distance Formula, just another parenthesis section with z's under the Square Root

Multiple Choice

What would be the distance between (2, 4, 5) and (1, 10, -6)? [rounded to 3 decimal places]

• -9.876

• 16.547

• 10.453

• 12.570

Multiple Choice

What would be the distance between (0, 11, 3.5) and (-2, -5, 7.4)? [rounded to 3 decimal places]

• 10.112

• 18.956

• 16.589

• 14.324

New Notes!

Make Sure You Write These Down!!!

Equation of a Sphere

(x-h)² + (y-k)² + (z-l)² = r²

Center located at ( h, k, l ) with Radius r.

Example 1

• What would be the equation of the Sphere with a Center at (1, -2, 4) and a Radius of 2?

• Plug the h, k, l, and r into the Sphere Equation: (x - h)² + (y - k)² + (z - l)² = r²

• (x - 1)² + (y - -2)² + (z - 4)² = 2²

• Simplify (if needed)

• (x - 1)² + (y + 2)² + (z - 4)² = 4

Multiple Choice

Example 2: Which of the following would be the correct Equation for a Sphere with a Center at (-1, 0, 3) and a Radius of 10?

• (x + 1)² + y² + (z - 3)² = 100

• (x - 1)² + y² + (z + 3)² = 100

• (z + 1)² - (x + 3)² - y² = 100

Multiple Choice

Example 3: What would be the equation for a Circle with a center of (8,3,7) and a Radius of 14?

• (x - 3)² + (y - 8)² + (z - 7)² = 196

• (x - 8)² + (y - 3)² + (z - 7)² = 196

• (x - 4)² + (y - 1.5)² + (z - 3.5)² = 196

That's all for this "mini-lesson"

If you haven't done so already, make sure you finish / turn-in our Wednesday Assignment. Don't Forget that we will be doing the Benchmark in Class tomorrow, it will be through MasteryConnect and the code will be posted in Classroom.

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