Question

A(-6,p), B(10,6) and C(30,q) and 3 collinear points. also 4q+5p=k. find the value of k.


help​

Answer 1

Step-by-step explanation:

$Answer ⬇️⬇️$

Refer to the above attachment ⬆️⬆️

Answer 2

Answer:

Given that the points A(1,0,−6),B(−3,p,q) and C(−5,9,6) are collinear.Let the point B divide the line segment AC in the ratio k:1, then by section formula the coordinates of the point B are

(

k+1

−5k+1

,

k+1

9k+0

,

k+1

6k−6

)

But the coordinates of the point B are (−3,p,q), so we have,

k+1

−5k+1

=−3,

k+1

9k+0

=p,

k+1

6k−6

=q

⇒−5k+1=−3k−3,

k+1

9k

=p,

k+1

6k−6

=q

⇒−5k+3k=−3−1,

k+1

9k

=p, k+16k−6

=q⇒−2k=−4, k+19k=p, k+1

6k−6=q⇒k=2, k+19k=p, k+16k−6 =q⇒k=2,p= k+19k ,q= k+16k−6

⇒k=2,p= 2+19×2 ,q= 2+16×2−6

⇒k=2,p= 39×2

,q= 312−6⇒k=2,p=3×2,q= 36

∴k=2,p=6,q=2