Q. 14.3( 36 Votes )

<span lang="EN-US

Answer :

Let three vertices of the triangle be A, B and C

And the coordinates of third vertex be (x, y)


We have,


A ( - 4, 3),


B (4, 3) and


C (x, y)


We know that, in equilateral triangle the angle between two adjacent sides is 60 and all three sides are equal.


AB = BC = CA


AB2 = BC2 = CA2


Now, taking first two parts


AB2 = BC2


(4 + 4)2 + (3 - 3)2 = (x – 4)2 + (y – 3)2


64 + 0 = x2 + 16 – 8x + y2 + 9 – 6y


x2 + y2 – 8x – 6y = 39……. (ii)


Now, taking first and third parts;


AB2 = CA2


(4 + 4)2 + (3 - 3)2 = ( - 4 - x)2 + (3 – y)2


64 + 0 = 16 + x2 + 8x + 9 + y2 – 6y


x2 + y2 + 8x – 6y = 39……. (iii)


On subtracting Eq. (ii) from Eq. (iii),


We get:



x = 0


Now, by putting the value of x in Eq. (ii),


We get;


0 + y2 – 0 – 6y = 39


y2 – 6y – 39 = 0


y =


Solution of ax2 + bx + c = 0 is x =


y =







So, the points of third vertex are (0,3 + 4√3) or (3 - 4√3)


But given that, the origin lies in the interior of the ΔABC and the x - coordinate of third vertex is zero.


Then, y - coordinate of third vertex should be negative.



Hence, the required coordinate of third vertex,


C = [ c ≠ ]


Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Related Videos
Section FormulaSection FormulaSection Formula53 mins
Basics of Coordinate GeometryBasics of Coordinate GeometryBasics of Coordinate Geometry53 mins
Distance FormulaDistance FormulaDistance Formula52 mins
Doubt SessionDoubt SessionDoubt Session47 mins
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation
caricature
view all courses
RELATED QUESTIONS :

If A(1,5), B (-2,KC Sinha - Mathematics

The line segment KC Sinha - Mathematics

If the points (10KC Sinha - Mathematics

If the middle poiKC Sinha - Mathematics

Find the length oKC Sinha - Mathematics

The coordinates oKC Sinha - Mathematics

Find the distanceKC Sinha - Mathematics