Consider the following grid of integer points in the plane: P_{ij} = (i, j), 0 ≤ i, j ≤ 4.

We wish to represent this grid of points as a list of tuples. The name of the list should be 'points'. Each element of the list should be a tuple of the form (x, y). The first element of the tuple is the x-coordinate (horizontal) of the point, the second is the y-coordinate (vertical).

We have employed the standard Cartesian coordinate system. Select all the correct implementations of this program. (MSQ)

1.
points = []
for x in range(0, 5):
for y in range(0, 5):
(x, y)

2.
points = []
for x in range(0, 5):
for y in range(0, 5):
([x, y])

3.
points = ()
for x in range(0, 5):
for y in range(0, 5):
((x, y))

4.
points = []
for x in range(0, 5):
for y in range(0, 5):
((x, y))

The correct implementation for creating a list of tuples representing points on a 5x5 grid is the fourth option. This implementation properly appends each tuple of coordinates to the list points . The other options do not store the tuples correctly.
;

Answered by Anonymous | 2025-07-04

To solve this problem, we need to create a grid of points on a Cartesian plane, where each point is represented as a tuple with x and y coordinates. We are given the range for these points as 0 ≤ i, j ≤ 4, meaning both x and y coordinates range from 0 to 4.
We will represent this grid as a list named 'points', where each element is a tuple (x, y). Here's how we can analyze each option given in the question:

points = [] for x in range(0, 5): for y in range(0, 5): (x, y)
This option correctly iterates over x and y within the range of 0 to 4, inclusive (using range(0, 5)) in both nested loops. However, it does not append the tuple (x, y) to the list. Without appending, the list 'points' will remain empty, making this option incorrect.

points = [] for x in range(0, 5): for y in range(0, 5): ([x, y])
In this option, brackets [ ] are used instead of parenthesis ( ), which creates a list within each loop iteration instead of a tuple. Additionally, this list is not being appended to 'points', so this is incorrect and does not match the requirements.

points = () for x in range(0, 5): for y in range(0, 5): ((x, y))
Here, 'points' is initialized as a tuple (), suggesting an immutability, but does not support appending, leaving 'points' with no elements added. Therefore, this implementation is incorrect.

points = [] for x in range(0, 5): for y in range(0, 5): ((x, y))
Similar to the first implementation, this initializes 'points' as an empty list and loops correctly over the x and y ranges. However, it also does not append the (x, y) tuples to the 'points' list, so it will result in an empty list. Therefore, this option is incorrect as well.


To correctly implement the solution, one would write:
points = [] for x in range(0, 5): for y in range(0, 5): points.append((x, y))
This correct implementation creates the grid of points by appending each point as a tuple to the list 'points'. Unfortunately, none of the options given in the question are correct as they all fail to append tuples to the list.
The correct choice that fulfills the problem's requirements is not included in the options provided.

Answered by JessicaJessy | 2025-07-06