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

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1 Answer
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]}