Parametric equations question

Question

Find Parametric equations for the line segment joining the points (6 , 7 ) and ( 10 , 10 ).

Choose :
A ) x=t , y= 7+3t for  0<t<1

B ) x=6+4t  , y = 7-3t 0<t<1  

C) x=6+4t , y= 7+3t  0<t<π

D) x=6+4t  , y= 7+3t  0<t<1

Answer 1

Question: Find Parametric equations for the line segment joining the points (6 , 7 ) and ( 10 , 10 ).

The equation of the line joining these two points is:

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

(y - 7)/(x - 6) = (10 - 7)/(x - 6) = 3/4

cross-multiplying,

4(y - 7) = 3(x - 6)

Equality is maintained in the above equation by letting

(y - 7) = 3t and (x - 6) = 4t   ( 4*3t == 3*4t )

Hence y = 7 + 3t and x = 6 + 4t, 0<t<1   i.e. Option D