Problem: In this diagram a scheme is indicated for associating all the points of segment AB with those of segment Aβ²Bβ², and reciprocally. To describe this association scheme analytically let x be the distance from a point P on AB to D and let y be the distance from the associated point Pβ² of Aβ²Bβ² to Dβ². Then for any pair of associated points, if x=a,x+y equals:
Answer Choices:
A. 13a
B. 17aβ51
C. 17β3a
D. 417β3aβ
E. 12aβ34
Solution:
DP=x=aDβ²Pβ²=yPβ²Bβ²PBβ=41β
y=Dβ²Bβ²+Bβ²Pβ²=1+BPβ²=1+4PB
PB=4βx=4βa
y=1+4(4βa)=17β4a
x+y=17β3a
or
m=ΞxΞyβ=4β31β5β=β4sincexyβ35β41β
y=β4x+b5=β12+bb=17
y=β4x+17When x=a,x+y=17β3a
