Question

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

Explanation:

Step1: Find the difference in x - coordinates

Let $(x_1,y_1)=(-4,-4)$ and $(x_2,y_2)=(-1,2)$. The difference in x - coordinates $\Delta x=x_2 - x_1=-1-(-4)=3$.

Step2: Find the difference in y - coordinates

The difference in y - coordinates $\Delta y=y_2 - y_1=2-(-4)=6$.

Step3: Apply the Pythagorean theorem

The distance $d$ between two points is given by $d=\sqrt{(\Delta x)^2+(\Delta y)^2}$. Substitute $\Delta x = 3$ and $\Delta y = 6$ into the formula: $d=\sqrt{3^{2}+6^{2}}=\sqrt{9 + 36}=\sqrt{45}\approx6.71$.

Answer:

A. 6.71