Vector Coordinate Systems Worksheet

Which quadrant of the Cartesian plane contains points where both x and y coordinates are positive?

• Quadrant I

• Quadrant II

• Quadrant III

• Quadrant IV

If a point has a negative x-coordinate and a positive y-coordinate, in which quadrant does it lie?

• Quadrant I

• Quadrant II

• Quadrant III

• Quadrant IV

A point is located in Quadrant IV. What are the signs of its x and y coordinates?

• (+, +)

• (-, +)

• (-, -)

• (+, -)

What is the fixed point called in the polar coordinate system?

• Axis

• Vertex

• Pole (or origin)

• Focus

Based on the diagram, what do the variables r and θ represent in polar coordinates?

• r is the radius of a circle, θ is the area

• r is the directed distance from the pole, θ is the directed angle from the polar axis

• r is the x-coordinate, θ is the y-coordinate

• r is the slope, θ is the intercept

Which axis does the unit vector 𝑘̂ represent in the diagram?

• x-axis

• y-axis

• z-axis

• w-axis

Which of the following statements correctly describes the unit vectors i, j, and k in Cartesian coordinates?

• They are vectors of length 1 parallel to the x-, y-, and z-axes, respectively.

• They are vectors of length 2 parallel to the x-, y-, and z-axes, respectively.

• They are vectors of length 1 parallel to the y-, z-, and x-axes, respectively.

• They are vectors of length 1 parallel to the x-, y-, and w-axes, respectively.

Given the vector 3i + 5j + 4k, which component represents the movement along the y-axis?

• 5j

• 3i

• 4k

• 3j

Based on the diagram, which of the following pairs correctly represents the coordinates of a point in both Cartesian and Polar forms?

• (x, y) and (r, θ)

• (r, x) and (y, θ)

• (θ, r) and (y, x)

• (x, θ) and (r, y)

Given the Cartesian point (5, -12), what is the value of r in polar coordinates?

• 7

• 13

• 17

• 12