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

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)

Answer 2

Answer:

$(\frac{5}{4}, \frac{7}{4})$

Step-by-step 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:

$x = \frac{mx_2+nx_1}{m+n}$  and $y = \frac{my_2+ny_1}{m+n}$

m: n = 1:3

Now ,Substitute the values

$x = \frac{1(8)+3(-1)}{1+3}$

$x = \frac{5}{4}$

$y = \frac{1(4)+3(1)}{1+3}$

$y = \frac{7}{4}$

Thus the coordinates of C is $(\frac{5}{4}, \frac{7}{4})$

Hence  the coordinates of the point closest to point A are  $(\frac{5}{4}, \frac{7}{4})$