Question

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?

Answer 1

2sqrt41

Explanation:

Origin=(0,0)

Brenda wants to go from (-4,5) to (0,0) and then to (5,-4). So we need to calculate the distance from (-4,5) to (0,0), and the distance of (0,0) to (5,-4).

The distance formula is sqrt (x2-xs1)^2+(y2-y1`)^2.

So: sqrt (5-0)^2+(-4-0)^2

sqrt (5^2+-4^2)

sqrt 25+16

sqrt 41

Now we need to figure out the distance from (0,0) to (5,-4)

sqrt(0-5)^2+(0-(-4))^2

sqrt(-5^2+4^2)

sqrt 25+16

sqrt 41

sqrt 41+sqrt 41

2sqrt41

Answer 2

`\boxed{D = 6.4 units}`

Explanation:

She stops by (0,0)

She further needs to travel to (5,-4)

Let's calculate the distance using the Distance Formula:

Distance Formula =
`√((x2-x1)^2+(y2-y1)^2)`

D =
`√((5-0)^2+(-4-0)^2)`

D =
`√((5)^2+(-4)^2)`

D =
`√(25+16)`

D =
`√(41)`

D = 6.4 units

She needs to travel 6.4 units more.