pt. of division of line segment?

Question

Pt. of Division of line segment

Help Pls!
1. The segment joining (5,11) and (-3, -1) is to be divided into four equal parts. Find the points of division.

Answer 1

why not find the distance then mulitply it by .25, .50, .75

Answer 2

To divide the segment joining (a,b) to (c,d) into n equal parts, the points of division are (a + (k/n)*(c - a), b + (k/n)*(d - b)), for k = 1, 2, ... , n-1.

Answer 3

distance =sqr[ (5+3)^2 + (11+1)^2 ] = sqr(208) = 4sqr(13)
midpoint
x2 = -3 + 1/2 [ 8 ] = -3 + 4 = 1
y2 = - 1 + 1/2 (12) = - 1 + 6 = 5
(1,5)

first segment from (-3,-1)
x1 = = -3 + 1/4 [ 8 ] = -3 + 2 = -1
y1 = - 1 + 1/4 (12) = - 1 + 3 = 2
(-1,2)

x3= -3 + 3/4 [ 8 ] = -3 + 6 = 3
y3 = - 1 + 3/4 (12) = - 1 + 9 = 8
(3,8)

Answer 4

a million. locate eqt of line starting to be to be a member of a(-5,4) and b(4,-8) locate the place this cuts X axis , call m locate |am| & |mb| Ratio = |am| / |mb| 2. -8 --> 11 => + 19 on X +19 / 4 = 4 3/4 ..upload to X values a million --> 7 => +6 on Y +6 / 4 = a million a million/2....upload to Y values i.e. (-8,a million)-> ( -3 .seventy 5, 2.5) ->( a million, 4) etc 3. 6-->-3 => -9 on X -9-->-4 => +5 on Y A(6,-9)-> (-3,-4)->(-12,+a million) -> etc