SOLUTION: The segment joining F(-6,11) and G(3,4)is divided into four equal parts. Find the points of division. How can I find the points? Please explain in a detailed way because I really w

Question 1012383: The segment joining F(-6,11) and G(3,4)is divided into four equal parts. Find the points of division. How can I find the points? Please explain in a detailed way because I really want to understand the lesson!! Thank you!
Found 3 solutions by Alan3354, macston, fractalier:
Answer by Alan3354(69443)   (Show Source): You can put this solution on YOUR website!
The segment joining F(-6,11) and G(3,4)is divided into four equal parts. Find the points of division. How can I find the points?
-----------------
Find the x & y values separately.
Find the midpoint first. It's the average of the x & y values.
For x:
(-6 + 3)/2 = -3/2
For y:
(11 + 4)/2 = 15/2
--> Midpoint at MP (-3/2,15/2) or (-1.5,7.5)
-----------------------------------------------
Find the other 2 points the same way, using the MP and F, then MP and G.
Answer by macston(5194)   (Show Source): You can put this solution on YOUR website!
.
F=(-6,11); G=(3,4)
.
The x distance between F and G is
=
The y distance between F and G is
=
.
Since we want 4 equal parts, we divide the distance by 4:
x distance: 9/4
y distance: -7/4
.
Now starting at Point F, we want to move 9/4 in the x direction
and -7/4 in the y direction (call this point A, end of first quarter):
A=( -6+(9/4) , 11+(-7/4) )
A=( -15/4 , 37/4 }
.
From Point A, we move the same distance to point B (from F, halfway to G):
B=( (-15/4)+(9/4) , (37/4)+(-7/4) )
B=( -6/4 , 30/4 )
.
From point B to point C (from F to C is three quarters):
C=( (-6/4)+(9/4) , (30/4)+(-7/4) )
C=( 3/4 , 23/4 )
.
The four segments are:
F to A . (-6,11) to (-3 3/4, 9 1/4)
.
A to B . (-3 3/4, 9 1/4) to (-1 1/2, 7 1/2)
.
B to C . (-1 1/2, 7 1/2) to (3/4, 5 3/4)
.
C to G . (3/4, 5 3/4) to (3,4)

Answer by fractalier(6550)   (Show Source): You can put this solution on YOUR website!
If a line is divided into four equal parts, then I think you can see that the line was split in half, and then each half was again split in half, yielding four equal pieces.
If you understand that, then what we need to do is find the midpoint of a line three times.
The midpoint of the line connecting F(-6,11) and G(3,4) is the average of their x and y values...after all the point in the middle is halfway across on x and halfway up on the y...
So the midpoint is ((-6 + 3)/2, (11 + 4)/2) or (-3/2, 15/2). Call that point M for midpoint.
Then we find the midpoint of F and M the exact same way. Then again for M and G. Can you finish?
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