Question

What are the coordinates of the point that is 1/6 of the way from A(14, −1) to B(−4, 23)?

A) (11, 3)
B) (5, 11)
C) (8, 6)
D) (−1, 19)

Answer 1

What are the coordinates of the point that is 1/6 of the way from A(14, −1) to B(−4, 23)?
A) (11, 3)

Answer 2

Answer: The correct option is

(A) (11, 3).

Step-by-step explanation: We are given to find the co-ordinates of he point that is one-sixth of the way from A(14, −1) to B(−4, 23).

As shown in the attached figure below, let point P is one-sixth of the way from A to B.

Also, let P divides the the segment AB in the ratio m : n.

Then, we must have

`(m)/(m+n)=(1)/(6)\\\\\\\Rightarrow 6m=m+n\\\\\Rightarrow 6m-m=n\\\\\Rightarrow 5m=n\\\\\Rightarrow (m)/(n)=(1)/(5)\\\\\Rightarrow m:n=1:5.`

So, the point P divides AB in the ratio 1 : 5.

We know that

if a point divides the line segment joining the points (a, b) and (c, d) in the ratio m : n, then its co-ordinates are

`\left((mc+na)/(m+n),(md+nb)/(m+n)\right).`

Therefore, the co-ordinates of the point P will be

`\left((1*(-4)+5*14)/(1+5),(1*23+5*(-1))/(1+5)\right)\\\\\\=\left((-4+70)/(6),(23-5)/(6)\right)\\\\\\=\left((66)/(6),(18)/(6)\right)\\\\=(11,3).`

Thus, the required co-ordinates of the point is (11, 3).

Option (A) is CORRECT.