What Is the Locus of Vertex A in a Right Triangle with Hypotenuse 5 Units?

  • Thread starter Thread starter aisha
  • Start date Start date
  • Tags Tags
    Points
AI Thread Summary
In a right triangle ABC with a hypotenuse BC measuring 5 units, the locus of vertex A can be determined by recognizing that the hypotenuse serves as the diameter of the circumscribing circle. The circle's equation can be derived from the radius, which is half the hypotenuse, resulting in a radius of 2.5 units. This leads to the equation x^2 + y^2 = 6.25, which represents the set of points for vertex A. The discussion highlights confusion around deriving the locus and the relationship between the triangle's geometry and the circle. Understanding these concepts is crucial for solving locus problems in geometry.
aisha
Messages
584
Reaction score
0
In a right triangle ABC, the hypotenuse BC is 5 units. Determine an equation for the locus of points for the vertex A. What will a trace of these points look like? AHHHH all these locus questions I don't have a clue I drew the triangle with BC as the hypotenuse but I don't know what else to do. PLz help me someone please :redface:
 
Physics news on Phys.org
Geometric hint: In any right triangle, the hypotenuse is the diameter of the circumscribing circle- that is, a circle with the hypotenuse as diameter will pass through the right angle vertex.
 
Don't you mean radius?
 
I feel like I don't have enough information only 5 units, I see how a circle can be drawn around the right angle triangle with the diameter=hypotenuse but I don't know how to determine an equation for the set of points for the vertex A. What do I do?

Is this correct? x^2+y^2=6.25 for the equation
 
Last edited:

Thread 'Struggling to understand the concept of this question (ice cube in water optics question)'

TL;DR Summary: I came across this question from a Sri Lankan A-level textbook. Question - An ice cube with a length of 10 cm is immersed in water at 0 °C. An observer observes the ice cube from the water, and it seems to be 7.75 cm long. If the refractive index of water is 4/3, find the height of the ice cube immersed in the water. I could not understand how the apparent height of the ice cube in the water depends on the height of the ice cube immersed in the water. Does anyone have an...
View full post »
Thread 'Variable mass system : water sprayed into a moving container'

Thread 'Variable mass system : water sprayed into a moving container'

Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system $$M(t) = M_{C} + m(t)$$ $$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$ $$P_i = Mv + u \, dm$$ $$P_f = (M + dm)(v + dv)$$ $$\Delta P = M \, dv + (v - u) \, dm$$ $$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$ $$F = u \frac{dm}{dt} = \rho A u^2$$ from conservation of momentum , the cannon recoils with the same force which it applies. $$\quad \frac{dm}{dt}...
View full post »

Similar threads

To find the ratio of forces around a right triangle
Replies
2
Views
2K
Project Motion/Trigonometry Question
Replies
9
Views
2K
To find the magnitude of the resultant of forces around a triangle
Replies
4
Views
2K
Force pulling on a string at an angle with a block at the other end
Replies
2
Views
1K
What is the speed of the boat relative to the water?
Replies
6
Views
4K
Area of a Triangle Using Vectors.
Replies
19
Views
4K
Electric Field at Center of Equilateral Triangle
Replies
17
Views
3K
Area of interior triangle of pyramid normal to a side length
Replies
3
Views
2K
What is the net electrostatic force of the sphere at the origin?
Replies
3
Views
2K
Find Area of Sand Pile Base: 2.4m, 35° Repose
Replies
8
Views
3K

Hot Threads

Recent Insights

Back
Top