Question

Point Q is plotted on the coordinate grid. Point P is at (30, -30). Point R is vertically above point Q. It is at the same distance from point Q as point P is from point Q.

Which of these shows the coordinates of point R and its distance from point Q?

The options provided, "0" and "7," do not provide complete information for the coordinates and distance of point R. Additional information is needed to answer the question accurately.

Answer 1

To convert polar coordinates to Cartesian coordinates, use the equations x = r × cos(θ) and y = r × sin(θ). You can then measure the distance between two points in Cartesian coordinates using the distance formula. A chameleon's position on a screen can be described similarly in both coordinate systems.

Step-by-step explanation:

The question pertains to concepts in polar coordinates and their conversion to Cartesian coordinates, as well as measuring distances in these coordinate systems.

To find Cartesian coordinates from polar coordinates, you can use the conversion formulas:
x = r × cos(θ)
y = r × sin(θ)

For the polar coordinate (47/3, 5.50 m), the Cartesian coordinates would be calculated as follows:
x = (47/3) × cos(5.50)
y = (47/3) × sin(5.50). Since the angle is given in radians, make sure your calculator is set appropriately.

For the points P₁ (2.500 m, π/6) and P₂ (3.800 m, 27π/3), their Cartesian coordinates are found similarly, and then the distance between them can be calculated using the distance formula for Cartesian coordinates:
Distance = √((x₂ - x₁)² + (y₂ - y₁)²).

A chameleon on a lanai screen located at (2.000 m, 1.000 m) is √((2.000)² + (1.000)²) m from the corner of the screen. In polar coordinates, its location would be the distance from the origin (the corner of the screen) r and the angle it makes with the positive x-direction θ, which can be found using tan⁻¹(y/x).