Problema Solution
if the segment whose end points are A(-3,-4) and B(6,7) is divided into 7 equal parts. Find the 2 out of 6 points of division which are nearer to the 2 given points.
Answer provided by our tutors
If (x1, y1) and (x2, y2) are the endpoints of the segment, and k is the fractional part of the segment you want, the coordinates of the point is given by the formula:
x1 = -3, y1 = -4
x2 = 6, y2 = 7
For the point that is near (-3, -4) we have k = 1/7 and the point is:
(x , y) = (-3 + (1/7)(6 - (-3)), -4 + (1/7)(7 - (-4)))
(x, y) = (- 12/7, -17/7)
(x, y) = (- 1 5/7, - 2 3/7)
For the point that is near (6, 7) we have k = 6/7 and the point is:
(x , y) = (-3 + (6/7)(6 - (-3)), -4 + (6/7)(7 - (-4)))
(x , y) = (33/7, 38/7)
(x , y) = (4 5/7, 5 3/7)