Space Coordinates, Spheres, and Sandwhiches

Front

What are the three coordinates needed to represent a point in 3D space?

Back

x, y, z

Front

What is the formula for finding the midpoint of a line segment between two points P1(x1, y1, z1) and P2(x2, y2, z2)?

Back

Midpoint = ((x1 + x2)/2, (y1 + y2)/2, (z1 + z2)/2)

Front

What is the center of a sphere given by the equation x^2 + y^2 + z^2 = 4x + 10y - 10z?

Back

(2, 5, -5)

Front

What is a panini?

Back

A type of sandwich that is grilled and pressed.

Front

What is the definition of a sphere in 3D space?

Back

A set of points that are all the same distance (radius) from a central point (center).

Front

How do you convert the equation of a sphere from standard form to center-radius form?

Back

Complete the square for x, y, and z terms.

Front

What is the distance formula in 3D space between two points P1(x1, y1, z1) and P2(x2, y2, z2)?

Back

Distance = √((x2 - x1)² + (y2 - y1)² + (z2 - z1)²)

Front

What is the definition of a sandwich?

Back

A food item consisting of two or more slices of bread with fillings in between.

Front

What is the significance of the coordinates (latitude, longitude, altitude)?

Back

They represent a point's position in 3D space relative to the Earth's surface.

Front

What is an iceberg lettuce?

Back

A type of lettuce that has a crisp texture and mild flavor.