Help!

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?

Hi Logic!

a) (-4,5) to (0,0)

b) (0,0) to (5,-4)

\(d=\sqrt{(x_1-x_2)^2+(y_1-y_2)^2}\)

\(d_a=\sqrt{(-4-0)^2+(5-0)^2}=\sqrt{16+25}\\ d_a=\sqrt{41}\)

\(d_b=\sqrt{(0-5)^2+(0-(-4))^2}=\sqrt{25+16}\\ d_b=\sqrt{41}\)

\(d_a+d_b=2\cdot \sqrt{41}=12.806..\)

Brenda has to travel 12,806 times the local unit of length.

Is the origin on the way the origin of the coordinate system?
Or does Brenda travel back to the starting point?

Then:

twice (-4,5) to (5,-4)

\(d=2\cdot \sqrt{(-4-5)^2+(5-(-4))^2}=2\cdot\sqrt{81+81}\\ d=2\cdot \sqrt{2\cdot 3^4}=2\cdot 3^2\cdot \sqrt{2}\\ \color{blue}d=18\cdot\sqrt{2}=25.4558..\)

Brenda has to travel 25.456 times the local unit of length.

Greatings

  !