Final answer:
The parameterization of the line segment connecting the points (2,7) and (1,4) is described by the equations x(t) = 2 - t and y(t) = 7 - 3t, where t varies from 0 to 1.
Step-by-step explanation:
To find the parameterization for the line segment connecting the points (2,7) and (1,4), we need to express both the x and y coordinates as functions of a parameter, often denoted as t. A common method to parameterize a line segment between two points P (x1, y1) and Q (x2, y2) is to use the following linear equations:
- x(t) = (1 - t)x1 + tx2
- y(t) = (1 - t)y1 + ty2
Here, t will vary from 0 to 1. Substituting the given points into these equations, we get:
- x(t) = (1 - t)*2 + t*1
- y(t) = (1 - t)*7 + t*
Therefore, the parameterization of the line segment is:
- x(t) = 2 - t
- y(t) = 7 - 3t
This parameterization gives us the x and y coordinates of any point on the line segment as t varies from 0 (at point (2,7)) to 1 (at point (1,4)).