Final answer:
To find parametric equations through a point and perpendicular to a line, determine the equation of the line, find the slope, determine the negative reciprocal of the slope, choose a point on the line, and write the parametric equations.
Step-by-step explanation:
To find parametric equations through a point and perpendicular to a line, we need to follow these steps:
- First, determine the equation of the given line.
- Next, find the slope of the given line by using the formula 'slope = (y2 - y1) / (x2 - x1)', where (x1, y1) and (x2, y2) are any two points on the line.
- Then, determine the negative reciprocal of the slope. This will give you the slope of the perpendicular line. Let's call this slope 'm'.
- Now, choose any point on the given line and let its coordinates be (x, y). This will be the point through which the parametric equations pass.
- Finally, write the parametric equations using the point-slope form: x = x + mt and y = y + mt, where (x, y) are the coordinates of the chosen point and 't' is the parameter that represents different values along the line.
The geometric interpretation of these parametric equations is that the line they represent passes through a specific point and is always perpendicular to the given line. So, as 't' varies, the point (x, y) moves along the perpendicular line.