Question

use the pythagorean theorem to find the length of the segment with endpoints p(1,2) and q(5,4). (check out example 1 from the pythagorean theorem and distance formula lesson.)

Explanation:

Step1: Find horizontal and vertical distances

The horizontal distance $\Delta x$ between $P(1,2)$ and $Q(5,4)$ is $x_2 - x_1=5 - 1=4$. The vertical distance $\Delta y$ is $y_2 - y_1=4 - 2 = 2$.

Step2: Apply Pythagorean theorem

The length $d$ of the line - segment between two points is given by $d=\sqrt{(\Delta x)^2+(\Delta y)^2}$. Substitute $\Delta x = 4$ and $\Delta y=2$ into the formula: $d=\sqrt{4^2 + 2^2}=\sqrt{16 + 4}=\sqrt{20}\approx4.47$.

Answer:

4.47