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