Final answer:
The coordinates of point L are found using the section formula for the internal division of a line segment in the ratio 3:1, which results in the coordinates (1, 3).
Step-by-step explanation:
The student asks to find the coordinates of point L given that segment PZ has point L such that PZ:LZ has a ratio of 3:1, and the coordinates of P (-2,-3) and Z (2,5). To find the coordinates of point L, we use the section formula in coordinate geometry that applies to internal division of a segment in a given ratio. Since the ratio is 3:1, we can denote it as m:n where m=3 and n=1. Thus, the coordinates of point L (x, y) can be calculated as:
- x = (mx2 + nx1) / (m + n)
- y = (my2 + ny1) / (m + n)
Plugging in the values, we get:
- x = (3*2 + 1*(-2)) / (3 + 1) = (6 - 2) / 4 = 1
- y = (3*5 + 1*(-3)) / (3 + 1) = (15 - 3) / 4 = 3
Therefore, the coordinates of point L are (1, 3).