Circumcenter poi (triangle) - confuced

[ssj-gohan]

im having some problems with my homework, I basically know what things to do, but not really how to apply them. Were doing things like circumcenter, poi, medians, etc of a triangle.

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The first questions states:

You decide to put a distress beacon on a buoy inside the trainge that is equidistant from all 3 vertices of the triangle to warn incoming ships. Your assistant has calculated (2,3) as the approriate point. Verify whether or not this is the correct point to place the beacon. Why would you want the beacon to be equidistant from all three verities?

-I know for this problem i would use circumcenter to solve, tried so many things and my answers were, (4,3) for AB and AC, and (3.5, 4.5) for BA and BC, i don't know if their right I am so confused.

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You've located Polly! She was carried out to sea on a small boat and was picked up by a rescue plane at the coordinates (8,5). if the plane is going to fly straight to Skwaera will it cross over the triangle? If so, for how long will they be over the waters of the triangle? The plane flies at 200km/hr.

-Just know u need interception, distance to island and distance to interception, don't know how to solve though

 

[HallsofIvy]

Do you KNOW where the vertices of the triangle are? If you don't then there is no way to answer the question. If you do, then the best way to decide IF (2,3) is equidistant from the vertices is to actually calculate the distance from (2,3) to each of the vertices. Are the distances the same?

Okay, Polly is at (8,5). Where is "Skwaera"? If you know the coordinates of that point, then you can find the equation of the line. To find where that line crosses each side of the triangle, find the equation of the line between the two vertices and solve the "simultaneous" equations.

 

[wais]

Hello, it seems like you are having some trouble with your homework. Don't worry, geometry can be confusing at times. Let's start with the first question about the distress beacon. The correct point to place the beacon is called the circumcenter, which is the point that is equidistant from all three vertices of the triangle. In this case, the coordinates (2,3) are not correct because they do not satisfy this condition. To find the correct point, you can use the formula for the circumcenter: the intersection of the perpendicular bisectors of the sides of the triangle. This will give you the coordinates of the point where the beacon should be placed. As for why it should be equidistant from all three vertices, this ensures that the beacon can be seen and reached from any direction, providing a warning for incoming ships.

Moving on to the second question about Polly and the rescue plane, you are correct in thinking that you need to use the concept of interception. The rescue plane will cross over the triangle if its path intersects with the triangle. To find out if this will happen, you can use the slope-intercept form of a line to represent the path of the plane and then find the point of intersection with the triangle. If the plane's path does intersect with the triangle, you can then use the distance formula to calculate the distance it will travel over the waters of the triangle. Remember that distance = speed x time, so you can use the distance and the plane's speed to find the time it will be over the waters of the triangle. I hope this helps you with your homework. Keep practicing and don't hesitate to ask for help when you need it. Good luck!