Question

A fly lands on one wall of a room. The lower - left corner of the wall is selected as the origin of a two - dimensional Cartesian coordinate system. If the fly is located at the point having coordinates (2.00, 1.00)m,

1. how far is it from the origin?
2. What is its location in polar coordinates?

Short answer

The distance between two points in the xy plane = 2.24 m

so the polar coordinates$r=2.24\overline{)\underline{26.6^o}}$

Step-by-step solution

Definition of vector

A vector is a quantity that has both a direction and a magnitude, and is used to determine the relative location of two points in space.

Step 2:Formula

If vector A = a₁i + a₂j + a₃k and vector B = b₁i + b₂j + b₃k then the displacement of AB = (b₁ - a₁)i + (b₂ - a₂)j + (b₃ - a₃)k

If vector A = x₁i + y₁j + z₁k and vector B = x₂i + y₂j + z₂k then the displacement of

The Pythagorean theorem and the definition of tangent will use for calculation

$d=\sqrt{{\left(x_2-x_1\right)}^2+{\left(y_2-y_1\right)}^2+{\left(z_2-z_1\right)}^2}$

The Distance Between Two Points

Take the wall as the xy plane so that the coordinates are x = 2.00 m and y= 1.00 m; and the fly is located at point P. The distance between two points in the xy plane

$d=\sqrt{{\left(2.00-0\right)}^2+{\left(1.00-0\right)}^2}=2.24m$

The Angle Between Two Points

$\theta ={\tan }^{-1}\frac{1.00}{2.00}=26.6^o$so the polar coordinates$r=2.24\overline{)\underline{26.6^o}}$