Answer:
To find three lattice points that have a distance of 5 from the point (-32) and do not form a horizontal or vertical segment we can use the following steps:
1. Start by considering the lattice points that are within a distance of 5 from the given point (-32). This forms a square or diamond-shaped area around the point (-32).
2. In this case we can consider a 5x5 square around the point (-32 where each point on the lattice is represented by its coordinates (x).
3. Iterate through each lattice point within the square and calculate its distance from the point (-32) using the distance formula: distance = sqrt((x - (-3))^2 + (y - 2)^2).
4. Check if the calculated distance is 5 for any lattice point. If the distance is 5 check if the line connecting this point with the point (-32) is neither horizontal nor vertical.
5. If the distance is 5 and the line connecting the two points is neither horizontal nor vertical you have found a valid lattice point.
6. Repeat the process until you find three valid lattice points with a distance of 5 from (-32) and not forming a horizontal or vertical segment.