Rakimi is playing a video game. Her character is on a quest to vanquish an evil sorcerer in a castle surrounded by cannons. Her character is an archer whose powerful arrows can reach a range of 6 units. The location of the objects in the game are stored in a computer program in terms of (x,y) coordinates. The archer is at (5,4); cannon A is at (8,7); cannon B (2,-1); and cannon C is at (9,0).
1. Which cannon can the archer's arrow reach?
2. At what location (in terms of coordinates), does the archer must go so that her arrow can reach the evil sorcerer who is located at (-4,-3)?
I really don't know how to solve it, I already spend many hours in researching about this kind of problem and about trying some formulas, please help me. Also it states the I need to illustrate it using RCP. What is RCP? Thank you very much in advance.
1. use the distance formula to find if the archer is within range of any cannon
2. any location within a circle of radius 6, centered at (-4,-3)
... the equation of the circle is ... (x + 4)^2 + (y + 3)^2 = 36
don't know RCP
Thank you once again!
RPC stands for rectangular coordinate plane
To determine which cannon the archer's arrow can reach, we need to calculate the distance between the archer's location and each cannon. If the distance is within the range of the archer's arrow (6 units), then the cannon can be reached.
To calculate the distance between two points (x1, y1) and (x2, y2) on a coordinate plane, we can use the distance formula:
Distance = sqrt((x2 - x1)^2 + (y2 - y1)^2)
Let's calculate the distances between the archer's location (5, 4) and each cannon:
For cannon A (8, 7):
Distance_A = sqrt((8 - 5)^2 + (7 - 4)^2) = sqrt(3^2 + 3^2) = sqrt(18) ≈ 4.24
For cannon B (2, -1):
Distance_B = sqrt((2 - 5)^2 + (-1 - 4)^2) = sqrt(-3^2 + (-5)^2) = sqrt(9 + 25) = sqrt(34) ≈ 5.83
For cannon C (9, 0):
Distance_C = sqrt((9 - 5)^2 + (0 - 4)^2) = sqrt(4^2 + (-4)^2) = sqrt(16 + 16) = sqrt(32) ≈ 5.66
Since the range of the archer's arrow is 6 units, we can see that cannon A and cannon C are within range, while cannon B is outside the range.
So, the archer's arrow can reach cannon A and cannon C.
Now, to find the location where the archer must go to reach the evil sorcerer at (-4, -3) with her arrow, we can reverse the distance calculation.
Let's represent the coordinates of the location the archer must go to as (x, y). The distance between the archer's current location (5, 4) and (-4, -3) must be less than or equal to the range of the archer's arrow (6 units).
Distance = sqrt((-4 - 5)^2 + (-3 - 4)^2)
By solving the equation for Distance ≤ 6, you can find the possible locations (x, y) where the archer can go to reach the evil sorcerer.
Regarding "RCP," it seems to be a typo or misunderstanding. There is no widely known acronym "RCP" related to this problem. It might be referring to a specific concept or notation within the context that is not mentioned in the provided information.
I hope this helps clarify the solution approach to the problem. If you have any further questions, please let me know.