Final answer:
To find the coordinates of endpoint N, we can use the concept of partitioning a directed segment. The ratio of 5:2 means that the segment is divided into 5 equal parts and 2 equal parts. Using the formula N(x, y) = [(5 * P(x1, y1)) + (2 * M(x2, y2))]/(5 + 2), we can substitute the given values and simplify to find N(1/7, (79/49)).
Step-by-step explanation:
To find the coordinates of endpoint N, we can use the concept of partitioning a directed segment. The ratio of 5:2 means that the segment is divided into 5 equal parts and 2 equal parts. Since we need to find the coordinates of N, which is the endpoint after the partition, we can use the formula:
N(x, y) = [(5 * P(x1, y1)) + (2 * M(x2, y2))]/(5 + 2)
Substituting the given values into the formula, we get: N(x, y) = [(5 * (3, 23/7)) + (2 * (-7, -6))]/(5 + 2)
Simplifying further, we get: N(x, y) = [(15, (115/7)) + (-14, -12)]/7
Adding the vectors, we get: N(x, y) = (1, (79/7))/7
Dividing by 7, we get the coordinates of N: N(1/7, (79/49))