Question

An air show is scheduled for an airport located on a coordinate system measured in miles. The air traffic controllers have closed the airspace, modeled by a quadratic equation, to non-air show traffic. The boundary of the closed airspace starts at the vertex at (10, 6) and passes through the point (12, 7). A commuter jet has filed a flight plan that takes it along a linear path from (–18, 14) to (16, –13). Which system of equations can be used to determine whether the commuter jet’s flight path intersects the closed airspace?
THESE ARE THE MULTIPLE CHOICE
please i need help nowww

Answer 1

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.