A fly lands on one wall of a room. The lower left-hand corner of the wall is selected as the origin of a two-dimensional Cartesian coordinate system. The fly is located at the point having coordinates (1.80, 1.15) m.
(a) How far is it from the corner of the room?
Pythagoras theorem states for a right angled triangle where C is the hypothenuse:
A²+B²=C*sup2;
Can you take it from here, unless you have parts (b) and (c)?
2.136
To find the distance from the corner of the room to the point where the fly is located, we can use the Pythagorean theorem. The distance is the hypotenuse of a right triangle with the coordinates (1.80, 1.15) as one of the vertices and the corner of the room (0, 0) as the other vertex.
The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b). Mathematically, it can be written as:
c^2 = a^2 + b^2
In this case, we have the coordinates of the point where the fly is located (1.80, 1.15). The horizontal distance (a) from the corner of the room to the point is 1.80 m, and the vertical distance (b) is 1.15 m. So, we can substitute these values into the Pythagorean theorem:
c^2 = (1.80)^2 + (1.15)^2
c^2 = 3.24 + 1.3225
c^2 = 4.5625
To find c, we take the square root of both sides:
c = √4.5625
c = 2.135 m
Therefore, the distance from the corner of the room to the point where the fly is located is approximately 2.135 meters.