The video tutorial introduces graphing in three dimensions, starting with the basics of the distance formula in two dimensions and extending it to three dimensions by adding a z-coordinate. It explains how to graph points in 3D space using x, y, and z axes, and provides a visual analogy of moving along the edges of a box. The tutorial also covers the distance formula in 3D, which is an extension of the Pythagorean theorem, and introduces the midpoint formula for three-dimensional points. The instructor plans to use computer tools to aid visualization and understanding.

What is the basic distance formula in two dimensions?

• X2 - X1 squared + Y2 - Y1 squared, then square root

• X2 - X1 squared + Y2 - Y1 squared

• X2 - X1 + Y2 - Y1

• X2 + X1 squared + Y2 + Y1 squared

Tags

CCSS.HSG.GPE.B.7

In three dimensions, which additional variable is included in the distance formula?

• W

• Z

• T

• V

Tags

CCSS.HSG.GPE.B.7

Which axes are used to graph points in three dimensions?

• X, Z, and W

• X, Y, and W

• Y, Z, and W

• X, Y, and Z

Tags

CCSS.5.G.A.1

How do you graph the point (1, 2, 4) in three dimensions?

• Move 1 unit along X, 2 units up Y, and 4 units forward Z

• Move 4 units along X, 2 units up Y, and 1 unit forward Z

• Move 1 unit along X, 4 units up Y, and 2 units forward Z

• Move 2 units along X, 1 unit up Y, and 4 units forward Z

Tags

CCSS.5.G.A.2

What shape can help visualize three-dimensional graphs?

• Box

• Sphere

• Cylinder

• Pyramid

Tags

CCSS.5.G.A.1

What is the formula for the distance between two points in three dimensions?

• X2 - X1 squared + Y2 - Y1 squared + Z2 - Z1 squared, then square root

• X2 - X1 squared + Y2 - Y1 squared + Z2 - Z1 squared

• X2 - X1 squared + Y2 - Y1 squared

• X2 - X1 + Y2 - Y1 + Z2 - Z1

Tags

CCSS.HSG.GPE.B.7

What is the midpoint formula in three dimensions?

• (X1 + X2) / 2, (Y1 + Y2) / 2, (Z1 - Z2) / 2

• (X1 + X2) / 2, (Y1 + Y2) / 2, (Z1 + Z2) / 2

• (X1 + X2) / 2, (Y1 + Y2) / 2

• (X1 - X2) / 2, (Y1 - Y2) / 2, (Z1 - Z2) / 2

Tags

CCSS.HSG.GPE.B.6

What is the result of applying the distance formula to the points (1, 2, 4) and (3, 5, -1)?

• Square root of 35

• Square root of 45

• Square root of 55

• Square root of 50

Tags

CCSS.HSG.GPE.B.7

How do you find the midpoint between (1, 2, 4) and (3, 5, -1)?

• (2, 3.5, 1.5)

• (2, 3.5, 1.5)

• (2, 3.5, 1.5)

• (2, 3.5, 1.5)

Tags

CCSS.HSG.GPE.B.6

What theorem is the distance formula based on?

• Archimedes' Theorem

• Newton's Theorem

• Euclidean Theorem

• Pythagorean Theorem

Tags

CCSS.HSG.GPE.B.7