An air show is scheduled for an airport located on a coordinate system measured in miles. The air traffic controllers have close

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An air show is scheduled for an airport located on a coordinate system measured in miles. The air traffic controllers have close

d 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
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Mathematics

1 answer:

Leona [12.6K] · Answer 1 · 2026-02-20T10:21:27+03:00

The system of equations that can determine if the commuter jet’s flight path crosses the restricted airspace is:

y = \frac{1}{4}(x - 10)^2 + 6 (i)
y = \frac{-27}{34}x - \frac{5}{17} (ii)

Here's why:

The closed airspace boundary is defined by points (10, 6) and (12, 7).

The commuter jet’s linear path runs from (-18, 14) to (16, -13).

Equation (i) describes the boundary since it fits both (10, 6) and (12, 7):

For (10, 6):
\frac{1}{4}(10-10)^2 + 6 = 6 (true)

For (12, 7):
\frac{1}{4}(12-10)^2 + 6 = 1 + 6 = 7 (true)

Equation (ii) represents the commuter jet’s path as it fits both (-18, 14) and (16, -13):

For (16, -13):
-13 = \frac{-27}{34} \times 16 - \frac{5}{17} = -13 (true)

For (-18, 14):
14 = \frac{-27}{34} \times (-18) - \frac{5}{17} = 14 (true)

By solving this system, we can confirm that the jet’s flight path intersects the closed airspace.