Question

1. use the pythagorean theorem to find the distance between (-7, 7) and (5, -4). round to the nearest tenth

Explanation:

Step1: Find the difference in x - coordinates

Let $(x_1,y_1)=(-7,7)$ and $(x_2,y_2)=(5, - 4)$. The difference in x - coordinates $\Delta x=x_2 - x_1=5-(-7)=12$.

Step2: Find the difference in y - coordinates

The difference in y - coordinates $\Delta y=y_2 - y_1=-4 - 7=-11$.

Step3: Apply the Pythagorean theorem

The distance $d$ between two points is given by $d=\sqrt{(\Delta x)^2+(\Delta y)^2}$. Substitute $\Delta x = 12$ and $\Delta y=-11$ into the formula: $d=\sqrt{12^{2}+(-11)^{2}}=\sqrt{144 + 121}=\sqrt{265}$.

Step4: Round the result

$\sqrt{265}\approx16.3$.

Answer:

$16.3$