Question

IN ABC IS EQUALATRERAL TRIANGLE WHERE VERTEX A HAS CODINATE (0, √3) FIND THE CODINATE OF B AND C​

Answer 1

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In figure, △ABC is an equilateral triangle with coordinate of B and C as B(1,0) and C(5,0). Find the coordinate of vertex A.

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Solution

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Correct option is A)

The ordinates of both B & C are 0.

So, BC= (abscissa of B−abscissa of C)=(5−1)=4units=a

The side of equilateral ΔABC.

∴ Its height=

2

3

a=

2

3

×4=2

3

units.

Also, the mid point of BC=(

2

5+1

,

2

0+0

)=(3,0).

Now, ΔABC is equilateral and BC is on the x-axis.

So, the abscissa of A will be the mid point of BC.

The ordinate of A will be the height of ΔABC from the mid point of BC.

∴ The coordinates of A are (3,2

3

).