What are the 6 point that divide the line between (-5,4) and (13,22)?

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1 Answer
CW
Apr 29, 2018

see explanation.

Explanation:

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If the line #PS# is divided into 6 congruent segments, there should be 5 points in between #PS#, namely, #P_1,P_2,P_3,P_4 and P_5#, as shown in the figure.
As #PP_1, P_1P_2, P_2P_3,P_3P_4,P_4P_5, and P_5S# are equidistant,
#=> x=(13-(-5))/6=3#
similarly, #y=(22-4)/6=3#
#=> P_1=(x_1,y_1)=(-5+x,4+y)=(-5+3,4+3)=(-2,7)#
similarly, #P_2=(x_2,y_2)=(x_1+x,y_1+y)=(-2+3,7+3)=(1,10)#
#P_3=(x_3,y_3)=(x_2+x,y_2+y)=(1+3,10+3)=(4,13)#
#P_4=(x_4,y_4)=(x_3+x,y_3+y)=(4+3,13+3)=(7,16)#
#P_5=(x_5,y_5)=(x_4+x,y_4+y)=(7+3,16+3)=(10,19)#

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