How do you find the coordinates of the other endpoint of a segment with the given Endpoint: (1,5) midpoint: (1,-6)?

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Answer 1 · 2016-05-20T14:00:53

Start point $" "->P_s->(x_s,y_s)" "->" "(1,-17)$

The distance from mid to end is the same distance from start to mid
as mid point is the mean point

Let end point be $P_e$

Let mean point be $P_m$

Let start point be $P_s$
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Mid to end $-> P_e-P_m$

Start to mid $-> P_m-P_s$

$color(green)("As distance from mid to each end is the same")$

we have $P_m-P_s= P_e-P_m$ .......(1)

Multiply equation (1) by (-1) so that $P_s$ is positive

$-P_m+P_s = +P_m - P_e$

Add $P_m$ to both sides

$P_s=P_m+P_m-P_e$

$P_s=2P_m-P_e$

$P_s->(x_s,y_s)$

$x_s=2(x_m)-x_e" "->" "2(1)-1=1$

$y_s=2(y_m)-y_e" "->" "2(-6)-5=-17$

$P_s->(x_s,y_s)" "->" "(1,-17)$