Question

1. use the pythagorean theorem to find the distance between (-7, 0) and (-9, 2). round to the nearest tenth

Explanation:

Step1: Identify coordinates

Let $(x_1,y_1)=(-7,0)$ and $(x_2,y_2)=(-9,2)$.

Step2: Calculate horizontal and vertical distances

The horizontal distance $a=\vert x_2 - x_1\vert=\vert-9-(-7)\vert=\vert-9 + 7\vert = 2$.
The vertical distance $b=\vert y_2 - y_1\vert=\vert2 - 0\vert=2$.

Step3: Apply Pythagorean Theorem

The distance $d$ between two points is given by $d=\sqrt{a^{2}+b^{2}}$. Substitute $a = 2$ and $b = 2$ into the formula: $d=\sqrt{2^{2}+2^{2}}=\sqrt{4 + 4}=\sqrt{8}\approx2.8$.

Answer:

$2.8$