Problem: In this diagram a scheme is indicated for associating all the points of segment AB with those of segment A′B′, 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 P′ of A′B′ to D′. Then for any pair of associated points, if x=a,x+y equals:
Answer Choices:
A. 13a
B. 17a−51
C. 17−3a
D. 417−3a​
E. 12a−34
Solution:
DP=x=aD′P′=yP′B′PB​=41​
y=D′B′+B′P′=1+BP′=1+4PB
PB=4−x=4−a
y=1+4(4−a)=17−4a
x+y=17−3a
or
m=ΔxΔy​=4−31−5​=−4sincexy​35​41​
y=−4x+b5=−12+bb=17
y=−4x+17When x=a,x+y=17−3a
