Question

1. constructing the distance formula

altitude (ft)
distance from the continental divide (ft)
write: use the pythagorean theorem, a² + b² = c², to create an equation you could use to solve for d and (x₂, y₂).
d² = __________

Explanation:

Step1: Identify horizontal and vertical distances

The horizontal distance is the difference in x - coordinates: $x_2 - x_1$. The vertical distance is the difference in y - coordinates: $y_2 - y_1$.

Step2: Apply Pythagorean Theorem

In the right - triangle formed by the horizontal, vertical distances and the line segment of length d, if $a=x_2 - x_1$ and $b = y_2 - y_1$ and $c = d$, then $d^{2}=(x_2 - x_1)^{2}+(y_2 - y_1)^{2}$ according to $a^{2}+b^{2}=c^{2}$.

Answer:

$(x_2 - x_1)^{2}+(y_2 - y_1)^{2}$