Question

Show that x=x1+(x2-x1)t, y=y1+(y2-y1)t, -∞ 12 years ago

Answer 1

it is clearly linear...now replace t with 0 and 1 to show that the two points are hit.

Answer 2

@amistre64
Can u pls suggest how to go about this one.....

Answer 3

define a direction vector between the points

Answer 4

given a point (a,b), and a vector <p,q>

the parametric line formed by then is simple:

x = a + pt
y = b + qt

Answer 5

I have used the method suggested by "Math???" but am not sure if it is right. We have not been taught to use vectors in solving such questions

Answer 6

or solve for t such that: t = (x-a)/p = (y-b)/q

Answer 7

it would be good to know what you HAVE been taught to put this into context, otherwise there are a myriad of different ways to approach it

Answer 8

another method would be to solve for t in terms of x, and sub that into the t in y to undo the parameter

Answer 9

x = a + pt, t = (x-a)/p

y = b + qt
= b + q(x-a)/p

Answer 10

We are using the book "Calculus - Graphic, Numerical and Algebraic" by Finney, Demana, Waits and Kennedy

Answer 11

We have been taught to solve by either putting in values of by expressing both in terms of t and then equating them and getting a final equation

Answer 12

define the point slope of the line between the given points, and compare that to the undoing of the parameter setup; if they are equal, they are the same ....

Answer 13

can u pls show how this is to be done.....i am struck with only this one. I have done the rest of the homework...

Answer 14

make 't' the subject in both equations and equate them. You'll get the equation of the line.

Answer 15

@kelvinltr
Can u pls show the actual working

Answer 16

i did show the work ...

Answer 17

it would be helpful if you could get your hands dirty by either attempting what has been suggested, or asking question about what might be confusing you about it.

Answer 18

equation of a line passing through (x1,y1) and (x2,y2) is

\[\frac{ x-x1 }{ x2-x1 }=\frac{ y-y1 }{ y2-y1 }\\\]
let

\[t=\frac{ x-x1 }{ x2-x1 }=\frac{ y-y1 }{ y2-y1 }\\\]

then make x and y the subjects of the two equations to get the equations given in the sum

Answer 19

I did convert both in terms of t and got the first equation you have written

\[t=\frac{ x-x1 }{ x2-x1 } and t=\frac{ y-y1 }{ y2-y1 }\]

From this I got
\[\frac{ x-x1 }{ x2-x1 }=\frac{ y-y1 }{ y2-y1 }\]

Answer 20

Now what to do further???

Answer 21

the slope from (x1,y1) to (x2,y2) can defined to be (y2-y1)/(x2-x1)

point slope form of a line is then:

(y-a) = (y2-y1)/(x2-x1) (x-b) ; for any point (a,b); choose the point (x1,y1)

(y-y1) = (y2-y1)/(x2-x1) * (x-x2)

equate that to the undoing of the parameters:

t = (x-x1)/(x2-x1)

y = y1 + (y2-y1)/(x2-x1) * (x-x1)

(y-y1) = (y2-y1)/(x2-x1) * (x-x1)

Answer 22

might have a typo in there :)

Answer 23

@amistre64
@kelvinltr
thanks for your help.!! Finally by adding up all ideas and working, I think I got the answer in the form I wanted. Now only my teacher will tell if it is right or not....Thanks again!!

Answer 24

:) good luck