Question

Point A is located at (0, 4), and point B is located at (−2, −3). Find the point that is 1 over 4 the distance from point A to point B.
(-1, 0.75)
(-0.75, 2)
(-0.5, 2.25)
(-0.25, 3)

Answer 1

The answer is (-0.5, 2.25).

Explanation:

A = (0,4)

B = (-2,-3)

The line joining the two points from A to B can be represented as a vector:

r (x) = A + x*(B - A)  ,  where  0<= x <= 1

Now, r (x) can be written as:

r (x) = (0,4) + x[ (-2,-3) - (0,4) ] = (0,4) + x (-2,-7)

Assuming x to be 1/4 (given)

x(1/4) = (0,4) + 1/4* (-2,-7) = (0 -1/2, 4  -7/4) = (-1/2, 9/4)  

= (−0.5, 2.25)

Answer 2

Solution

Find the mid point of A and B.

The mid point of A and B is (-1. 0.5)

Now find mid point of (0, 4) and (-1, 0.5)

= [(0 + (-1)/2 , (4 +0.5)/2 ]

= (-1/2, 4.5/2)

= (-0.5, 2.25)

The answer is (-0.5, 2.25)

Thank you.