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

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

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Answer 1 · 2018-03-16T07:31:29

$6$ $6$ coordinates are $(- \frac{2}{7}, \frac{54}{7})$ $(-2/7,54/7)$ , $(\frac{10}{7}, \frac{66}{7})$ $(10/7,66/7)$ , $(\frac{22}{7}, \frac{78}{7})$ $(22/7,78/7)$ , $(\frac{34}{7}, \frac{90}{7})$ $(34/7,90/7)$ , $(\frac{46}{7}, \frac{102}{7})$ $(46/7,102/7)$ and $(\frac{58}{7}, \frac{114}{7})$ $(58/7,114/7)$ .

Explanation:

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

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

Now the coordinates of the point that divides the length between the two points $(x_{1}, y_{1})$ $(x_1,y_1)$ and $(x_{2}, y_{2})$ $(x_2,y_2)$ in the ratio of $l : m$ $l:m$ is

$(\frac{l x_{2} + m x_{1}}{l + m}, \frac{l y_{2} + m y_{1}}{l + m})$ $((lx_2+mx_1)/(l+m),(ly_2+my_1)/(l+m))$

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

$(\frac{6 \cdot - 2 + 1 \cdot 10}{7}, \frac{6 \cdot 6 + 1 \cdot 18}{7})$ $((6*-2+1*10)/7,(6*6+1*18)/7)$ or $(- \frac{2}{7}, \frac{54}{7})$ $(-2/7,54/7)$

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

$(\frac{5 \cdot - 2 + 2 \cdot 10}{7}, \frac{5 \cdot 6 + 2 \cdot 18}{7})$ $((5*-2+2*10)/7,(5*6+2*18)/7)$ or $(\frac{10}{7}, \frac{66}{7})$ $(10/7,66/7)$

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

$(\frac{4 \cdot - 2 + 3 \cdot 10}{7}, \frac{4 \cdot 6 + 3 \cdot 18}{7})$ $((4*-2+3*10)/7,(4*6+3*18)/7)$ or $(\frac{22}{7}, \frac{78}{7})$ $(22/7,78/7)$

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

$(\frac{3 \cdot - 2 + 4 \cdot 10}{7}, \frac{3 \cdot 6 + 4 \cdot 18}{7})$ $((3*-2+4*10)/7,(3*6+4*18)/7)$ or $(\frac{34}{7}, \frac{90}{7})$ $(34/7,90/7)$

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

$(\frac{2 \cdot - 2 + 5 \cdot 10}{7}, \frac{2 \cdot 6 + 5 \cdot 18}{7})$ $((2*-2+5*10)/7,(2*6+5*18)/7)$ or $(\frac{46}{7}, \frac{102}{7})$ $(46/7,102/7)$

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

$(\frac{1 \cdot - 2 + 6 \cdot 10}{7}, \frac{1 \cdot 6 + 6 \cdot 18}{7})$ $((1*-2+6*10)/7,(1*6+6*18)/7)$ or $(\frac{58}{7}, \frac{114}{7})$ $(58/7,114/7)$

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]}

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

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