Find the third vertex of equilateral triangle, Mathematics

Assignment Help:

If two vertices of an equilateral triangle are (0, 0) and (3, 0), find the third vertex. [Ans: 3/2 , 3/√ 3/2  or 3/2, -3√ 3/2]

Ans:    OA = OB = AB

OA2 = OB2 = AB2

OA2 = (3-0)2 + 0 = 9

OB2 = x2 + y2

AB2 = (x-3)2 + y2 = x2 + y2 - 6x + 9

OA2 = OB2 = AB2

OA2 = OB2 & OB2 = AB2

9 = x2 + y2 ⇒ y2 = 9 - x2

x2 + y2 - 6x + 9 = 9

x2 + 9-x2 - 6x + 9 = 9

6x = 9              x= 3/2

y2 = 9 - (3/2)2 = 9-9/4 = 36-9/4=27/4

y =      ± 3√3/2 

∴ Third vertex is (3/2,3√3/2) or (3/2, -3√3/2)


Related Discussions:- Find the third vertex of equilateral triangle

Math on a spot, compare: 643,251: 633,512: 633,893. The answer is 633,512.

compare: 643,251: 633,512: 633,893. The answer is 633,512.

Geometry Question, Does the Angle-Side Relationship Theorm work for all tri...

Does the Angle-Side Relationship Theorm work for all triangles or just a certain type of triangle? Does is correspond with the orthocenter of a triangle?

What is universal set, A non-empty set or group of which all the sets under...

A non-empty set or group of which all the sets under concern are subsets is known as the universal set. In any part of application of set theory, all the sets under concern might l

State demorgans law and prove it using the truth table, State DeMorgan's la...

State DeMorgan's law. Prove it using the truth table.   Ans: DeMorgan's law defines that    (i)  (x ∨ y)' = x' ∧ y' (ii)  (x ∧ y)' = x' ∨ y'      Now let us dr

Porportions, how do you solve for porportions?

how do you solve for porportions?

Inequalities and intervals, What inequalities and intervals are? If it is g...

What inequalities and intervals are? If it is given that a real number 'p' is not less than another real number 'q', we understand that either p should be equal to q or

Homogeneous odes, how do you solve a homogeneous ode that''s not in a multi...

how do you solve a homogeneous ode that''s not in a multiplication or division form

Find out a vector that is orthogonal to the plane, A plane is illustrated b...

A plane is illustrated by any three points that are in the plane.  If a plane consists of the points P = (1, 0,0) , Q = (1,1,1) and R = (2, -1, 3) find out a vector that is orthogo

Write Your Message!

Captcha
Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd