Answer:
2[tex]\sqrt{41}[/tex] units is the distance that Brenda is going to travel.
Step-by-step explanation:
Given that:
Brenda starts from point [tex](-4,5)[/tex] to [tex](5,-4)[/tex]
Let point P [tex](-4,5)[/tex] and Q [tex](5,-4)[/tex].
But given that she need to stop by origin O[tex](0, 0)[/tex].
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
:
[tex]D = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
For PO:
[tex]x_2 = 0\\x_1 = -4\\y_2 = 0\\y_1 = 5[/tex]
[tex]PO = \sqrt{(0-(-4))^2+(0-5)^2}\\\Rightarrow PO = \sqrt{(4)^2+(5)^2} = \sqrt{41}\ units[/tex]
Similarly, For OQ:
[tex]x_2 = 5\\x_1 = 0\\y_2 = -4\\y_1 =0[/tex]
[tex]OQ = \sqrt{(5-0)^2+(-4-0)^2}\\\Rightarrow OQ = \sqrt{(5)^2+(4)^2} = \sqrt{41}\ units[/tex]
So, the total distance traveled = PO + OQ = [tex]\sqrt{41}+\sqrt{41}=2\sqrt{41}\ units[/tex]
2[tex]\sqrt{41}[/tex] units is the distance that Brenda is going to travel.
