SOLUTION: Please can you help solve this probelm? Thanks... p(-3,4) and q(9,-4) are two points. Find the coordinates of the point k,m and n on [pq] such that /pk/=/km/=/mn/=/nq/.

Algebra ->  Length-and-distance -> SOLUTION: Please can you help solve this probelm? Thanks... p(-3,4) and q(9,-4) are two points. Find the coordinates of the point k,m and n on [pq] such that /pk/=/km/=/mn/=/nq/.      Log On


   

Question 74310: Please can you help solve this probelm? Thanks...
p(-3,4) and q(9,-4) are two points. Find the coordinates of the point k,m and n on [pq] such that /pk/=/km/=/mn/=/nq/.
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Since these segments are all equal, that means we're going to divide this line into equal parts. So we need to find the midpoint of pq.
Solved by pluggable solver: To find midpoint of segment connecting two point
The Coordinates of mid point of a line segment joining two points can be calculated using following formulas.

X coordinate of mid point is

X%5Bmid%5D=+%28X+coordinate_of_first_point+%2B+X+coordinate_of_first_point%29%2F2


X%5Bmid%5D+=%28-3%2B9%29%2F2


X%5Bmid%5D+=%28-3%2B9%29%2F2=3


Y coordinate of mid point is

Y%5Bmid%5D=+%28Y+coordinate_of_first_point+%2B+Y+coordinate_of_first_point%29%2F2


Y%5Bmid%5D+=%284%2B-4%29%2F2


Y%5Bmid%5D=%284%2B-4%29%2F2=0

Hence, The mid point of segment joining two point (-3,4) and (9,-4) is (3,0)

So (3,0) is the midpoint of pq. This means the coordinates of m is (3,0) since its right in the middle. Now lets find the midpoint of the midpoint, or in other words, find the point thats a quarter of a way there.
Solved by pluggable solver: To find midpoint of segment connecting two point
The Coordinates of mid point of a line segment joining two points can be calculated using following formulas.

X coordinate of mid point is

X%5Bmid%5D=+%28X+coordinate_of_first_point+%2B+X+coordinate_of_first_point%29%2F2


X%5Bmid%5D+=%28-3%2B3%29%2F2


X%5Bmid%5D+=%28-3%2B3%29%2F2=0


Y coordinate of mid point is

Y%5Bmid%5D=+%28Y+coordinate_of_first_point+%2B+Y+coordinate_of_first_point%29%2F2


Y%5Bmid%5D+=%284%2B0%29%2F2


Y%5Bmid%5D=%284%2B0%29%2F2=2

Hence, The mid point of segment joining two point (-3,4) and (3,0) is (0,2)

So at the quarter mark we have the point k(0,2). Now lets find the midpoint between the middle and the end, which is q(9,-4)
Solved by pluggable solver: To find midpoint of segment connecting two point
The Coordinates of mid point of a line segment joining two points can be calculated using following formulas.

X coordinate of mid point is

X%5Bmid%5D=+%28X+coordinate_of_first_point+%2B+X+coordinate_of_first_point%29%2F2


X%5Bmid%5D+=%283%2B9%29%2F2


X%5Bmid%5D+=%283%2B9%29%2F2=6


Y coordinate of mid point is

Y%5Bmid%5D=+%28Y+coordinate_of_first_point+%2B+Y+coordinate_of_first_point%29%2F2


Y%5Bmid%5D+=%280%2B-4%29%2F2


Y%5Bmid%5D=%280%2B-4%29%2F2=-2

Hence, The mid point of segment joining two point (3,0) and (9,-4) is (6,-2)

So the coordinates of n are (6,-2). So the coordinates are:
k=(0,2), m=(3,0), and n=(6,-2)
You can always graph these points and the segment to visually verify this.