12.1 - 3D Coordinate Systems

Suppose you start at the origin, move along the x-axis a distance of 8 units in the positive direction, and then move downward a distance of 1 unit. What are the coordinates of your position?

• (8, 0, 1)

• (0, 8, 1)

• (8, -1, 0)

• (8, 0, -1)

• (8, 1, 0)

Tags

CCSS.5.G.A.2

Find the midpoint of the line segment from P1(−10, 10, 5) to P2(2, 8, 3).

• (−4, 9, 4)

• (6, 0, −1)

• (−6, 0, 1)

• (4, −9, −4)

• (1, 9, −4)

Tags

CCSS.HSG.GPE.B.6

Find an equation of the set of all points equidistant from the points A(7, -8, -9) and B(-4, 2, -10).

• 11x - 10y + z = -37

• 10x - 11y = 0

• -11x - 10y + z = 37

• 11x - 10y - z = 37

• 11x - 10y + z = 37

Find the center and radius of the sphere.

• C(1, -4, 3), r = 4

• C(4, -4, 3), r = 2√2

• C(1, 4, 3), r = √2

• C(1, -4, 2), r = 2

• none of these

Tags

CCSS.HSG.GPE.A.1

Find the distance from (-10, 2, -8) to the xy-plane.

• 10

• 8

• 2

• 16

• 4

Tags

CCSS.6.NS.C.8

Find an equation of the sphere with center (8, -4, 8) that touches the xy-plane.

• (x - 8)² + (y + 4)² + (z - 8)² = 4096

• (x - 8)² + (y + 4)² + (z - 8)² = 64

• (x - 8)² + (y - 4)² + (z - 8)² = 8

• (x + 8)² + (y - 4)² + (z + 8)² = 64

• (x + 8)² - (y - 4)² - (z + 8)² = 64

Tags

CCSS.HSG.GPE.A.1

Write an equation that represents all points on and inside a circular cylinder of radius 6 with the y-axis as its axis.

• y² + z² < 36

• x² + z² ≤ 36

• x² + z² ≥ 36

• x² + y² ≤ 36

• x² + y² ≤ 6

Suppose you start at the origin, move along the x-axis a distance of 4 units in the positive direction, and then move downward a distance of 8 units. What are the coordinates of your position?

• (4, 0, -8)

• (0, 4, 8)

• (4, 8, 0)

• (4, 0, 8)

• (4, -8, 0)

Tags

CCSS.5.G.A.2

Find the midpoint of the line segment from P1(8, 10, -3) to P2(-2, 10, 7).

• (-5, 0, 5)

• (-3, -10, -2)

• (5, 0, -5)

• (3, 10, 2)

• (-3, 10, 2)

Tags

CCSS.HSG.GPE.B.6

Write an equation or inequality that represents a plane containing all points with equal x and y coordinates.

• y ≠ z

• x ≤ y

• x = y

• x ≥ y

• y = z

Tags

CCSS.HSA.CED.A.3