Final answer:
To determine points representing a line segment with a slope of 4/3 and a length of 15 units, start from an arbitrary point like (0,0) and use the slope to find the endpoint using the Pythagorean theorem.
Step-by-step explanation:
The question asks to determine the points which represent a line segment with a slope of 4/3 and a length of 15 units. To find points that define such a line segment, we would need to choose an arbitrary starting point. Without loss of generality, let's assume the starting point is the origin (0,0). Given the slope of 4/3, for every 3 units we move horizontally, we move 4 units vertically.
To find the endpoint, we will use the Pythagorean Theorem since a line segment with a slope forms a right triangle with its rise and run. The length of the line segment, which is the hypotenuse of the right triangle, is 15 units. The relationship is given by the equation a² + b² = c², where c is the length of the hypotenuse. Given the slope is 4/3, we substitute 4n for vertical movement (rise) and 3n for horizontal movement (run), where 'n' is a scaling factor. Substituting these into the Pythagorean Theorem and solving for 'n' gives us the distances we must travel in each direction.Once we have the distances, we can add them to the starting point coordinates (0,0) to find the endpoint of the line segment. The coordinates of the endpoint would be (3n, 4n). Since the line segment needs to have a length of 15 units, calculating 'n' accurately is crucial for determining the exact point.