The diagram shows several lines. You can only see part of the lines, but they actually continue forever in both directions 1. Which lines are images of line f under a translation?

The diagram shows several lines. You can only see part of the lines, but they actually continue for

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CameronVand21

10.09.2020

Mathematics

1. let r be the point with unknown x-coordinate. consider vectors $\overrightarrow{qr}=())=(x+14)$ and $\overrightarrow{rs}=(2-x).$

these vectors are colinear and

$\dfrac{\overrightarrow{qr}}{\overrightarrow{rs}}=\dfrac{3}{5}.$

then

$\dfrac{x+14}{2-x}=\dfrac{3}{5},\\ \\5(x+14)=3(2-x),\\\\5x+70=6-3x,\\\\8x=-64,\\\\x=-8.$

2. if you need correct formula, then

$\dfrac{x_r-x_q}{x_s-x_r}=\dfrac{m}{n},\\ \\n(x_r-x_q)=m(x_s-x_r),\\\\nx_r-nx_q=mx_s-mx_r,\\\\x_r(n+m)=mx_s+nx_q,\\\\x_r=\dfrac{mx_s+nx_q}{m+n}.$

answer: point r partitions the directed line segment from q to s in a m: n, the ratio to determine point r is

$x_r=\dfrac{mx_s+nx_q}{m+n}.$

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