Question

A dartboard of radius 10 units and the wall it is hanging on are represented using a two-dimensional coordinate system, with the board’s centre at coordinate (0,0). Variables x and y store the x-coordinate and the y-coordinate of a dart that hits the dartboard. Write a Python expression using variables x and y that evaluates to True if the dart hits (is within) the dartboard, and then evaluate the expression for these dart coordinates:

a) (0,0)
b) (10,10)
c) (6, 6)
d) (7,8)

Answer 1

The distance formula can be used to calculate the distance between the points where the dart hits the dartboard and the centre of the dartboard.

The distance of a point P(x, y) from the origin is given by \(\sqrt{x^2+y^2}\)

To calculate the square root, the equation can be raised to the power 0.5.

Program:

x = int(input('Enter X Coordinate: '))

y = int(input('Enter Y Coordinate: '))

dis = (x ** 2 + y ** 2) ** 0.5

#if dis is greater than 10, means that dart is more than 10 units away from the centre.

print(dis <= 10)

The output for the dart coordinates are as follows:

a) (0,0): True
b) (10,10): False
c) (6,6): True
d) (7,8): False