Final answer:
The point that is 2/5 of the way from (-1,3) to (6,-5) is found using linear interpolation and is calculated as (1.8, -0.2).
Step-by-step explanation:
To find the point that is (2/5) of the way from (-1,3) to (6,-5), we use the concept of linear interpolation in two dimensions. This method involves finding the horizontal and vertical distances between the two points, multiplying those distances by the fraction (2/5 in this case), and then adding the resulting values to the coordinates of the starting point.
First, calculate the total horizontal and vertical distances between the points:
- Horizontal distance: 6 - (-1) = 7
- Vertical distance: -5 - 3 = -8
Second, find 2/5 of each distance:
- (2/5) × horizontal distance = (2/5) × 7 = 2.8
- (2/5) × vertical distance = (2/5) × -8 = -3.2
Finally, add these values to the coordinates of the starting point (-1,3):
- X-coordinate: -1 + 2.8 = 1.8
- Y-coordinate: 3 - 3.2 = -0.2
Therefore, the point that is 2/5 of the way from (-1,3) to (6,-5) is (1.8, -0.2).