Mathematics: 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?

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Brenda is going from $(-4,5)$ to $(5,-4)$, but

flore9584

30.01.2022

2 $\sqrt{41}$ units is the distance that Brenda is going to travel.

Step-by-step 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 :

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

For PO:

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

$PO = \sqrt{(0-(-4))^2+(0-5)^2}\\\Rightarrow PO = \sqrt{(4)^2+(5)^2} = \sqrt{41}\ units$

Similarly, For OQ:

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

$OQ = \sqrt{(5-0)^2+(-4-0)^2}\\\Rightarrow OQ = \sqrt{(5)^2+(4)^2} = \sqrt{41}\ units$

So, the total distance traveled = PO + OQ = $\sqrt{41}+\sqrt{41}=2\sqrt{41}\ units$

2 $\sqrt{41}$ units is the distance that Brenda is going to travel.

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