Find a parametrization for the line segment with endpoints (5,2) and (-2, -4).
as t changes from 0 to 1,
x changes by -7
y changes by -6
x = 5-7t
y = 2-6t
To find a parametrization for the line segment with endpoints (5,2) and (-2, -4), we need to find a vector function that describes the line connecting these two points.
Let's set t as the parameter that varies along the line segment. The parameter t will go from 0 to 1, where t = 0 corresponds to the starting point and t = 1 corresponds to the ending point.
First, let's find the difference between the x-coordinates and y-coordinates of the endpoints:
Δx = -2 - 5 = -7
Δy = -4 - 2 = -6
Now, we can write the parametrization for the line segment as follows:
x(t) = 5 + Δx * t
y(t) = 2 + Δy * t
Substituting the values of Δx and Δy, we get:
x(t) = 5 - 7t
y(t) = 2 - 6t
So, the parametrization for the line segment with endpoints (5,2) and (-2, -4) is:
x(t) = 5 - 7t
y(t) = 2 - 6t
To find a parametrization for the line segment with endpoints (5,2) and (-2, -4), follow these steps:
1. Calculate the difference between the x-coordinates of the endpoints: Δx = (-2) - 5 = -7.
2. Calculate the difference between the y-coordinates of the endpoints: Δy = (-4) - 2 = -6.
3. Choose a parameter t that ranges from 0 to 1, representing the proportion of the distance traveled along the line segment.
4. Define the parametric equations for x and y using the following formulas:
x = x1 + t * Δx
y = y1 + t * Δy
where (x1, y1) represents the coordinates of one of the endpoints.
Plugging in the values, we have:
x = 5 + t * (-7)
y = 2 + t * (-6)
These equations will parametrize the line segment between (5,2) and (-2, -4), as t varies between 0 and 1.