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

2
`√(41)` units is the distance that Brenda is going to travel.

Explanation:

Given that:

Brenda starts from point
`(-4,5)` to
`(5,-4)`

Let point P
`(-4,5)` and Q
`(5,-4)`.

But given that she need to stop by origin O
`(0, 0)`.

So, she travels from P to O first and then goes form O to Q.

Please refer to the attached figure for better understanding.

We need to find the distance PO + OQ to find the total distance traveled by Brenda.

We can use Distance formula :

`D = √((x_2-x_1)^2+(y_2-y_1)^2)`

For PO:

`x_2 = 0\\x_1 = -4\\y_2 = 0\\y_1 = 5`

`PO = √((0-(-4))^2+(0-5)^2)\\\Rightarrow PO = √((4)^2+(5)^2) = √(41)\ units`

Similarly, For OQ:

`x_2 = 5\\x_1 = 0\\y_2 = -4\\y_1 =0`

`OQ = √((5-0)^2+(-4-0)^2)\\\Rightarrow OQ = √((5)^2+(4)^2) = √(41)\ units`

So, the total distance traveled = PO + OQ =
`√(41)+√(41)=2√(41)\ units`

2
`√(41)` units is the distance that Brenda is going to travel.