Need help on the problem below with 4 coordinate points.
"compute the round trip distance from your house (-2,5), then to your friends house (8,-1), to your uncle's house (2,-1), and then back to your house (-2,5)
Thanks....
just work with two at a time, and add up the distances.
Do you understand the distance formula?
To compute the round trip distance, you need to calculate the distance between each pair of consecutive points and then sum them up.
Let's break down the calculations step-by-step:
1. Start with the first pair of points: your house (-2,5) and your friend's house (8,-1).
To calculate the distance between two points, you can use the distance formula:
Distance = sqrt((x2 - x1)^2 + (y2 - y1)^2)
Using the formula, the distance between your house and your friend's house is:
Distance 1 = sqrt((8 - (-2))^2 + (-1 - 5)^2)
= sqrt(10^2 + (-6)^2)
= sqrt(100 + 36)
= sqrt(136)
2. Next, calculate the distance between your friend's house (8,-1) and your uncle's house (2,-1):
Distance 2 = sqrt((2 - 8)^2 + (-1 - (-1))^2)
= sqrt((-6)^2 + 0^2)
= sqrt(36)
= 6
3. Finally, calculate the distance between your uncle's house (2,-1) and your house (-2,5):
Distance 3 = sqrt((-2 - 2)^2 + (5 - (-1))^2)
= sqrt((-4)^2 + 6^2)
= sqrt(16 + 36)
= sqrt(52)
= 2*sqrt(13)
4. Add up the three distances to get the round trip distance:
Round Trip Distance = Distance 1 + Distance 2 + Distance 3
= sqrt(136) + 6 + 2*sqrt(13)
Therefore, the round trip distance from your house to your friend's house, to your uncle's house, and back to your house is sqrt(136) + 6 + 2*sqrt(13).