Question

Line segment AB has endpoints A(6, 4) and B(2, 6). Find the coordinates of the point that divides the line segment directed from A to B in the ratio of 1:3.

Answer 1

(3, 5.5)

Explanation:

Given the line segment AB with endpoints A(6, 4) and B(2, 6). If the coordinates of the point divide the line segment directed from A to B in the ratio of 1:3, then;

M(X, Y) = {(ax1+bx2)/a+b, ay1+by2/a+b}

X = ax1+bx2/a+b

X = 1(6) + 3(2)/1+3

X = 6+6/4

X = 12/4

X = 3

Similarly;

Y = ay1+by2/a+b

Y = 1(4)+3(6)/1+3

Y = 4+18/4

Y = 22/4

Y = 5.5

Hence the required coordinate is (3, 5.5)