Question

in the given figure ,∆ABC AND ∆AD are quadrilateral triangle on com.on base AC , each side of triangle being 2a unit , vertices A and C lies on x axis , vertices B and D lies on y axis , o is the mid point odlf AC and BD , find the coordinates of the point A,B,C,D​

Answer 1

Since the mid-point of AB is at the origin O and AB=2a

∴ OA=OB=a.

Thus, the coordinates of A and B are (a,0) and (−a,0) respectively.

Since triangles ABC. and ABC' are equilateral. Therefore, their third vertices C and C'

lie on the perpendicular bisector of base AB. Clearly, YOY is the perpendicular bisector

of AB. Thus, C and C' lie on Y-axis. Consequently, their x-coordinates are equal to Zero.

In △AOC,wehave

OA

2

+OC

2

=AC

2

⇒a

2

+OC

2

=(2a)

2

⇒OC

2

=4a

2

−a

2

⇒OC

2

=3a

2

OC=

3a

Similarly, by applying Pythagoras theorem in △AOC; we have OC

′

=

3a

Thus, the coordinates of C and C' are (0,

3

a)and(0,−

3

a)respectively.

Answer 2

Answer:

12345678898766543113578