the base BC of an equilateral triangle ABC lies on y axis the coordinates of point C are - Maths - Coordinate Geometry

Question

the base BC of an equilateral triangle ABC lies on y axis the
coordinates of point C are (0,-3) if the origin is the mid point of
the base , find the coordinates of the points A and B please do not
give links and give proper explanation

Amit Shukla · Accepted Answer

Dear Student,

given: ABC is an equilateral triangle BC lies on y-axis and origin is the midpoint of BC let the coordinates of B are (0,y), since it lies on y-axis therefore the coordinates of B are y-3/2=0 i e y=3 coordinates are (0,3) therefore BC = 3-(-3)=3+3=6 units OA is the perpendicular bisector of BC therefore the vertex A will lie on OA i e x-axis let the coordinates of A are (x,0) since ABC is an equilateral triangle AB = BC $A B^{2} = B C^{2} (x - 0)^{2} + (0 - 3)^{2} = 6^{2} x^{2} + 9 = 36 x^{2} = 36 - 9 = 27 x = \pm \sqrt{27} = \pm 3 \sqrt{3}$ thus the coordinates of A are $(3 \sqrt{3}, 0) o r (- 3 \sqrt{3}, 0)$ Regards

the base BC of an equilateral triangle ABC lies on y axis . the coordinates of point C are (0,-3). if the origin is the mid point of the base , find the coordinates of the points A and B.. please do not give links and give proper explanation