Problem: If the point (x,−4)(x,-4)(x,−4) lies on the straight line joining the points (0,8)(0,8)(0,8) and (−4,0)(-4,0)(−4,0) in the xyx yxy plane, then xxx is equal to
Answer Choices:
A. −2-2−2
B. 222
C. −8-8−8
D. 666
E. −6-6−6 Solution:
Equate the reciprocals of the slopes of the segments joining ( x,−4x,-4x,−4 ) with (0,8)(0,8)(0,8) and (−4,0)(-4,0)(−4,0) with (0,8)(0,8)(0,8) to get −x/12=4/8-x / 12=4 / 8−x/12=4/8. Hence x=−6x=-6x=−6.