determine a set of parametric equations to represent the line segment that begins at the point(-2,6) and ends at the point (10,-4)
x = -2 + 12t
y = 6 - 10t
0 <= t <= 1
To determine a set of parametric equations that represent the line segment, we can use the parameter t to indicate the position along the line segment between the two given points.
Let's assume t varies from 0 to 1, where t = 0 represents the starting point (-2,6) and t = 1 represents the ending point (10,-4).
To find the parametric equations, we need to express the x-coordinate and y-coordinate as functions of t. We can use the following formulas:
x = (1 - t) * x1 + t * x2
y = (1 - t) * y1 + t * y2
where (x1, y1) is the starting point (-2,6) and (x2, y2) is the ending point (10,-4).
Let's substitute the values into the formulas:
x = (1 - t) * (-2) + t * 10
y = (1 - t) * 6 + t * (-4)
Simplify the equations:
x = -2(1 - t) + 10t
y = 6(1 - t) - 4t
Therefore, the parametric equations that represent the line segment are:
x = -2(1 - t) + 10t
y = 6(1 - t) - 4t