Question

(A) a certain corner of a room is selected as the origin of a recrangular coordinate system. If a fly is crawling on an adjacent wall at a point having coordinates (2.0, 1.0), where the units are meters, what is the distance of the fly from the corner of the room?(B) express the location of the fly in polar coordinates.

Answer 1

The "corner origin" is basically saying the room is the 1st quadrant, having a coordinate of (0, 0). Based on the position of the fly (1.1, 1.5), draw it out... 1.1 units horizontally, and 1.5 units vertically. You've now made 2 sides of a right triangle and can now find the hypotenuse (or the joining side) by using the Pythagorean Theorem equation x^2 + y^2 = z^2, with x and y being the two sides: 1.1 and 1.5

So let's plug those values in
2^2 + 1^2 = z^2
4 + 1 = z^2
5= z^2

Take the square root of 5
z = 2.23 meters

(2,1,2.3)