Question

1. use the pythagorean theorem to find the distance between (-7, 9) and (-9, 2). round to the nearest tenth

Explanation:

Step1: Find the difference in x - coordinates

Let $(x_1,y_1)=(-7,9)$ and $(x_2,y_2)=(-9,2)$. The difference in x - coordinates $\Delta x=x_2 - x_1=-9-(-7)=-9 + 7=-2$.

Step2: Find the difference in y - coordinates

The difference in y - coordinates $\Delta y=y_2 - y_1=2 - 9=-7$.

Step3: Apply the Pythagorean Theorem

The distance $d$ between two points is given by $d=\sqrt{(\Delta x)^2+(\Delta y)^2}$. Substitute $\Delta x=-2$ and $\Delta y = - 7$ into the formula: $d=\sqrt{(-2)^2+(-7)^2}=\sqrt{4 + 49}=\sqrt{53}$.

Step4: Round the result

$\sqrt{53}\approx7.3$

Answer:

$7.3$