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If the line PSPS is divided into 6 congruent segments, there should be 5 points in between PSPS, namely, P_1,P_2,P_3,P_4 and P_5P1,P2,P3,P4andP5, as shown in the figure.
As PP_1, P_1P_2, P_2P_3,P_3P_4,P_4P_5, and P_5SPP1,P1P2,P2P3,P3P4,P4P5,andP5S are equidistant,
=> x=(13-(-5))/6=3⇒x=13−(−5)6=3
similarly, y=(22-4)/6=3y=22−46=3
=> P_1=(x_1,y_1)=(-5+x,4+y)=(-5+3,4+3)=(-2,7)⇒P1=(x1,y1)=(−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)P2=(x2,y2)=(x1+x,y1+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)P3=(x3,y3)=(x2+x,y2+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)P4=(x4,y4)=(x3+x,y3+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)P5=(x5,y5)=(x4+x,y4+y)=(7+3,16+3)=(10,19)
