Question

Demonstrate, using your own unique example, how to divide a segment by a given ratio. Be sure to provide coordinates and a ratio that does not have a numerator or denominator of 1.

Answer 1

Suppose we have two points, A= (1,2) and B=(2,5)
We need to divide the line segment AB obtained by joining these 2 points, in a ratio 2:3,
Then, to find the coordinates of the point (x,y) which will divide the line segment AB (x1,y1) and (x2,y2) we will use the formula,

x=(mx1 + nx2)/(m+n)
y=(my1 + ny2)/(m+n)
Where m:n is the ratio in which it divides

Thus, coordinates will be x= (2*1 + 3*2)/(2+3)
Or x = 8/5

And y = (2*2 + 5*3)/(2+3) = 19/5

Thus the coordinates of the point are (8/5, 19/5) which divide the line in 2:3 formed by coordinates (1,2) and (2,5)