Answer:
[tex]d=4\sqrt{5}\approx8.94[/tex]
Step-by-step explanation:
To find the distance between any two points, we can use the distance formula:
[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2[/tex]
Let (-1, -2) be (x₁, y₁) and let (-9, 2) be (x₂, y₂).
Substitute appropriately:
[tex]d=\sqrt{(-9-(-1))^2+(2-(-2))^2[/tex]
Evaluate:
[tex]d=\sqrt{(-8)^2+(4)^2[/tex]
Square and evaluate:
[tex]d=\sqrt{64+16}=\sqrt{80}=4\sqrt{5}\approx8.94[/tex]
Therefore, the distance between the two points is approximately 8.94 units.
