Answered

DRIVING An observer at point O is watching cars drive along a straight road from point A to point C. The observer believes that if he takes
an observation at point B so that ZAOB ZBOC then point B will be the midpoint of AC.
100
yds
500 yds
A
B
C
Is the observer correct? Show or explain the reasoning used to justify the answer.

DRIVING An observer at point O is watching cars drive along a straight road from point A to point C The observer believes that if he takes an observation at poi class=


Answer :

To determine whether point B is the midpoint of AC, we need to understand the conditions given:

1. The observer believes that if he takes an observation at point B such that ∠AOB = ∠BOC, then point B will be the midpoint of AC.

First, let's understand what it means for ∠AOB = ∠BOC. This implies that the observer is positioned equidistant from points A and B, and also equidistant from points B and C. So, if we draw perpendiculars from point B to the line AC at points X and Y, then BX = BY.

Now, let's examine the distances along the line AC:

- The distance from point A to point C is 500 yards.

- The observer is positioned at point B, 100 yards from point A.

Since the observer believes that ∠AOB = ∠BOC, it suggests that he perceives himself to be equidistant from A and B, and from B and C. This would mean that BX = 100 yards and BY = 100 yards.

However, the total distance from A to C is 500 yards, and the observer is only 100 yards away from point A. Therefore, point B cannot be the midpoint of AC.

So, the observer is incorrect in believing that point B is the midpoint of AC.

Other Questions