Answer:
![d=\sqrt{58}\approx7.6](https://tex.z-dn.net/?f=d%3D%5Csqrt%7B58%7D%5Capprox7.6)
Step-by-step explanation:
To find the distance between any two points, we can use the distance formula:
![d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2](https://tex.z-dn.net/?f=d%3D%5Csqrt%7B%28x_2-x_1%29%5E2%2B%28y_2-y_1%29%5E2)
Our first point, A, is at (1, 1) and our second point, B, is at (-2, 8).
Let's let A(1, 1) be (x₁, y₁) and B(-2, 8) be (x₂, y₂). Substitute this into the distance formula:
![d=\sqrt{(-2-1)^2+(8-1)^2](https://tex.z-dn.net/?f=d%3D%5Csqrt%7B%28-2-1%29%5E2%2B%288-1%29%5E2)
Subtract:
![d=\sqrt{(-3)^2+(7)^2](https://tex.z-dn.net/?f=d%3D%5Csqrt%7B%28-3%29%5E2%2B%287%29%5E2)
Square:
![d=\sqrt{9+49}](https://tex.z-dn.net/?f=d%3D%5Csqrt%7B9%2B49%7D)
Add:
![d=\sqrt{58}](https://tex.z-dn.net/?f=d%3D%5Csqrt%7B58%7D)
This cannot be simplified.
So, the distance between the two points is √58 or about 7.6 units.
And we're done!
So... where's my cookie :)?