Question

use the drop downs to answer the following questions about the distance between the points $(-5,1)$ and $(2,-1)$. what is the distance of the horizontal leg? what is the distance of the vertical leg? use the pythagorean theorem. what is the distance between the two points?

Explanation:

Step1: Calculate horizontal distance

The horizontal distance is the difference in \(x -\)coordinates. For points \((-5,1)\) and \((2,-1)\), \(|x_2 - x_1|=|2-(-5)| = 7\).

Step2: Calculate vertical distance

The vertical distance is the difference in \(y -\)coordinates. \(|y_2 - y_1|=|-1 - 1|=2\).

Step3: Apply Pythagorean theorem

Let \(a = 7\), \(b = 2\). By \(c=\sqrt{a^{2}+b^{2}}\), \(c=\sqrt{7^{2}+2^{2}}=\sqrt{49 + 4}=\sqrt{53}\).

Answer:

Horizontal leg: \(7\); Vertical leg: \(2\); Distance between points: \(\sqrt{53}\)