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The point whose coordinates are x=x(1)+t...

The point whose coordinates are `x=x_(1)+t(x_(2)-x_(1)), y=y_(1)+t(y_(2)-y_(1))` divides the join of (x, y) and `(x_(2), y_(2))` in the ratio

A

`(t)/(1+t)`

B

`(1+t)/(t)`

C

`(t)/(1-t)`

D

`(1-t)/(t)`

Text Solution

Verified by Experts

The correct Answer is:
C
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Knowledge Check

  • If the point (x_(1) +t[x_(2)-x_(1)], y_(1)+t[y_(2)-y_(1)]) divides the join of (x_(1), y_(1)) and (x_(2), y_(2)) internally, then

    A
    `t lt 0`
    B
    `0 lt t lt 1 `
    C
    `t gt 1 `
    D
    `t =1`

  • I : If O is the origin and if A(x_(1),y_(1)), B(x_(2), y_(2)) are two points then OA*OB*cos angleAOB=x_(1)x_(2)+ y_(1)y_(2) II. If O is the origin and if A(x_(1), y_(1)), B(x_(2), y_(2)) are two points then OA*OB * sin angleAOB=x_(1)x_(2)+y_(1)y_(2)

    A
    only I is true
    B
    only II is true
    C
    both I and II are true
    D
    neither I nor II are true

  • The coordinates of the midpoint joining P(x_(1),y_(1)) and Q(x_(2),y_(2)) is ....

    A
    `((x_(1)+x_(2))/(2),(y_(1)+y_(2))/(2))`
    B
    `((x_(1)-x_(2))/(2),(y_(1)+y_(2))/(2))`
    C
    `((x_(1)+y_(1))/(2),1)`
    D
    none

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