### Instruction: Brenda is going from $(-4,5)$ to $(5,-4)$, but she needs to stop by the origin on the way. How far does she have to travel?### Response: To find the total distance, I need to add the distances from $(-4,5)$ to $(0,0)$ and from $(0,0)$ to $(5,-4)$.
To find the distance between two points, I can use the distance formula, which is based on the Pythagorean theorem.
The distance formula says that the distance between $(x_1,y_1)$ and $(x_2,y_2)$ is $\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$.
So, the distance from $(-4,5)$ to $(0,0)$ is $\sqrt{(0-(-4))^2+(0-5)^2}$.
Simplifying, I get $\sqrt{16+25}=\sqrt{41}$.
Similarly, the distance from $(0,0)$ to $(5,-4)$ is $\sqrt{(5-0)^2+(-4-0)^2}$.
Simplifying, I get $\sqrt{25+16}=\sqrt{41}$.
Adding the two distances, I get $\sqrt{41}+\sqrt{41}=2\sqrt{41}$.
This is the exact distance, but I can also approximate it using a calculator.
$\sqrt{41}$ is about 6.4, so $2\sqrt{41}$ is about 12.8.