Question

A segment has endpoints a (-1, 1) and b (8, 4) .if the segment is divided into four equal parts, the coordinates of the point closest to point a are _____.

Answer 1

`((5)/(4), (7)/(4))`

Explanation:

Refer the attached diagram

We are given a segment AB which is divided into four equal parts by three points

Now we are supposed to find the coordinates of the point closest to point A.

So, the point C divides the line in the Ratio = 1:3

Coordinates of A =
`(x_1,y_1)= (-1,1)`

Coordinates of B =
`(x_2,y_2)= (8,4)`

Let the coordinates of C be (x,y)

Now we will use section formula:

`x = (mx_2+nx_1)/(m+n)` and
`y = (my_2+ny_1)/(m+n)`

m: n = 1:3

Now ,Substitute the values

`x = (1(8)+3(-1))/(1+3)`

`x = (5)/(4)`

`y = (1(4)+3(1))/(1+3)`

`y = (7)/(4)`

Thus the coordinates of C is
`((5)/(4), (7)/(4))`

Hence the coordinates of the point closest to point A are
`((5)/(4), (7)/(4))`

Answer 2

The cordinate of the point closest to point a will be the point that divides the line segment in the ration 1:3

Required cordinate is ((1(8) + 3(-1))/4, (1(4) + 3(1))/4) = ((8 - 3)/4, (4 + 3)/4) = (5/4, 7/4)