Which system of equations can be used to determine whether the commuter jet’s flight path intersects the closed airspace?
The answer is: The system of equations number three:
y=1/4(x-10)²+6 (i)
y=(-27/34)x-5/17 (ii)
The reason is shown below:
-The boundary of the closed airspace: (10,6); (12,7)
-Linear path of the commuter jet: (-18,14) to (16,-13)
y=1/4(x-10)²+6 (i)
y=(-27/34)x-5/17 (ii)
The first equation represents the boundary of the closed airspace, because the points (10,6) and (12,7) are contained in the equation:
-For (10,6), we have:
(i) 1/4(10-10)²+6
6=6 (The equation is satisfied)
-For (12,7):
7=1/4(12-10)²+6
7=4/4+6
7=1+6
7=7 (The equation is satisfied)
The equation (ii) represents the path of the commuter jet, because the points (-18,14) and (16,-13) are contained in the equation:
-For(16,-13):
-13=(-27/34)x16-5/7
-13=-13 (The equation is satisfied)
-For (-18,14):
14=(-27/34)x(-18)-5/7
14=14 (The equation is satisfied)
Therefore, by resolving the system of equations, we know that the commuter jet’s flight path intersects the closed airspace.
