Question

the helicopter travels at a constant speed along the path shown in the cartesian plane below. determine the coordinates of the point where the helicopter passed over the border. (-43,55) (-22,-29)

Explanation:

Step1: Find the equation of the line

The equation of a line passing through two points $(x_1,y_1)=(-43,55)$ and $(x_2,y_2)=(-22,-29)$ is given by the two - point form $y - y_1=\frac{y_2 - y_1}{x_2 - x_1}(x - x_1)$. First, calculate the slope $m=\frac{y_2 - y_1}{x_2 - x_1}=\frac{-29 - 55}{-22+43}=\frac{-84}{21}=- 4$. Then the equation of the line is $y - 55=-4(x + 43)$, which simplifies to $y-55=-4x - 172$ or $y=-4x - 117$.

Step2: Assume the border is the x - axis ($y = 0$)

Set $y = 0$ in the line equation $0=-4x - 117$.

Step3: Solve for x

Add $4x$ to both sides: $4x=-117$. Then $x =-\frac{117}{4}=-29.25$.

Answer:

$(-29.25,0)$