Question

two students are flying drones in straight lines:
drone 1 flies from (1, 2) to (3, 6)
drone 2 flies from (2, 5) to (4, 9)
are their flight paths parallel, perpendicular, or neither?
a parallel paths
b perpendicular paths
c neither
d their paths cross but not at 90°

Explanation:

Step1: Calculate slope of Drone 1

The slope formula is $m=\frac{y_2 - y_1}{x_2 - x_1}$. For Drone 1 with points $(1,2)$ and $(3,6)$, we have $m_1=\frac{6 - 2}{3 - 1}=\frac{4}{2}=2$.

Step2: Calculate slope of Drone 2

For Drone 2 with points $(2,5)$ and $(4,9)$, using the slope formula $m=\frac{y_2 - y_1}{x_2 - x_1}$, we get $m_2=\frac{9 - 5}{4 - 2}=\frac{4}{2}=2$.

Step3: Determine relationship of paths

Since $m_1 = m_2=2$, the flight - paths are parallel.

Answer:

A. Parallel paths