Question

What are the x- and y-coordinates of point E, which partitions the directed line segment from A to B into a ratio of 1:2?

A. x=−1,y=3
B. x=0,y=1
C. x=1,y=0
D. x=2,y=−3

Answer 1

The question is about finding a point that divides a line segment in a 1:2 ratio using the section formula, but it cannot be solved without the coordinates of the end points of the line segment.

Step-by-step explanation:

The student is asking about the partitioning of a directed line segment in a given ratio, which is a concept from coordinate geometry. The partitioning process involves finding a point that divides a line segment into a specific ratio, in this case, 1:2. To solve this, one could use the formula for section formula, which in a two-dimensional space for a line divided in the ratio m:n is given by ((m • x2 + n • x1) / (m + n), (m • y2 + n • y1) / (m + n)), where (x1, y1) and (x2, y2) are the coordinates of the endpoints of the line segment. However, since no specific coordinates are provided, it is not possible to provide the coordinates of point E without additional information.