What are 6 coordinates that equally divide the line between (-2,6) and (10,18)?

enter image source here

1 Answer
Shwetank Mauria
Mar 16, 2018

#6# coordinates are #(-2/7,54/7)#, #(10/7,66/7)#, #(22/7,78/7)#, #(34/7,90/7)#, #(46/7,102/7)# and #(58/7,114/7)#.

Explanation:

#6# coordinates that divide the line between given two points equally, divide the length between them in #7# equal parts.

Hence, the ratios in which each of these points will divide the complete length are #1:6#, #2:5#, #3:4#, #4:3#, #5:2# and #6:1#.

Now the coordinates of the point that divides the length between the two points #(x_1,y_1)# and #(x_2,y_2)# in the ratio of #l:m# is

#((lx_2+mx_1)/(l+m),(ly_2+my_1)/(l+m))#

Hence the coordinates of point that divides the line between #(-2,6)# and #(10,18)# in the ratio #1:6# are

#((6*-2+1*10)/7,(6*6+1*18)/7)# or #(-2/7,54/7)#

the coordinates of point that divides the line in ratio #2:5# are

#((5*-2+2*10)/7,(5*6+2*18)/7)# or #(10/7,66/7)#

the coordinates of point that divides the line in ratio #3:4# are

#((4*-2+3*10)/7,(4*6+3*18)/7)# or #(22/7,78/7)#

the coordinates of point that divides the line in ratio #4:3# are

#((3*-2+4*10)/7,(3*6+4*18)/7)# or #(34/7,90/7)#

the coordinates of point that divides the line in ratio #5:2# are

#((2*-2+5*10)/7,(2*6+5*18)/7)# or #(46/7,102/7)#

the coordinates of point that divides the line in ratio #6:1# are

#((1*-2+6*10)/7,(1*6+6*18)/7)# or #(58/7,114/7)#

graph{((x+2)^2+(y-6)^2-0.1)((x-10)^2+(y-18)^2-0.1)((x+2/7)^2+(y-54/7)^2-0.1)((x-10/7)^2+(y-66/7)^2-0.1)((x-22/7)^2+(y-78/7)^2-0.1)((x-34/7)^2+(y-90/7)^2-0.1)((x-46/7)^2+(y-102/7)^2-0.1)((x-58/7)^2+(y-114/7)^2-0.1)(y-x-8)=0 [-16.26, 23.74, 2.32, 22.32]}

Related questions
Impact of this question
963 views around the world
You can reuse this answer
Creative Commons License