Question

if -5,3 and 5,3 are two vertices of an equilateral triangle, then find the coordinates of the third vertex, given that orgin lies inside the triangle (Take √3 = 1.7)​

Answer 1

• Answer:

Therefore, The Coordinates of the THIRD VERTEX is: ( 5, -3 )

• Explanation:

Calculate the midpoint of the given vertices:

MidPoint = ( -5 + 5/2, 3 + 3/2 )

MidPoint = ( 0, 3 )

• Calculate the distance between the given vertices:

Distance = √( -5 -5 )^2 + ( 3 - 3 )^2

Distance = √( -10 )^2 + (0)^2

Distance = √100

Distance = 10

• Calculate the side length of the equilateral triangle:

Side Length = 10/√3

Side Length = 10/1.7

Side Length = 5.88

• Calculate the height of the Third Vertex:

Height = √3/2 * Side Length

Height = 1.7/2 * 5.88

Height = 5

• Calculate the Coordinates of the Third Vertex:

Since the origin lies inside the triangle, The Third Vertex will have a Positive X-Coordinate and a Negative Y-Coordinate.

• Now, Let the Third Vertex Be:

( x, y )

• Using the MidPoint Formula now we have:

x = -5 + x/2

y = 3 + y/2

• Solve for X and Y, we now get:

x = 5

y = -3

• Draw a conclusion:

Hence, The Coordinate of the Third Vertex is: ( 5, -3 )

I hope this helps!