Discussion
The parametric representation of the line segment between the position vectors \(P_{1}(2, 3)\) and \(P_{2}(5, 4)\) is given as
Answer: C
The line segment from P1(2, 3) to P2(5, 4) is \(P(t) = P_{1} + t(P_{2} - P_{1})\), with t from 0 to 1.
\[ x(t) = 2 + t(5 - 2) = 2 + 3t \]
\[ y(t) = 3 + t(4 - 3) = 3 + t \]
So the third option is correct. The first option lets t grow without limit and gives a ray not a segment, the second has the wrong coefficients 10 and 12, and the fourth is not a parametric form of the line.
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