Question

The parametric equations below describe the line segment that joins the points P1(x1,y1) and P2(x2,y2). Find parametric equations to represent the line segment from (-3, 5) to (1, -2). x = x1 + (x2 – x1)t y = y1 + (y2 – y1)t 0 ≤ t ≤ 1

Answer 1

x=-3+4t\\

y =5-7t

Explanation:

we are given that when two point (x1,y1) and (x2,y2) are joined the parametric equation representing the line segment would be

`x = x_1 + (x_2 - x_1)t y = y_1 + (y_2 - y_1)t, 0 \leq ≤t \leq ≤ 1`

Our points given are

`(-3, 5) to (1, -2)`

So substitute the values to get

`x=-3+(1+3)t =-3+4t\\y = 5+(-2-3)t =5-7t`

Hence parametric equations for the line segment joining the points

(-3,5) and (1,-2) is

`x=-3+4t\\y =5-7t`