Question

A(-3,0) and B(3,0) are the vertices of an equilateral AABC. Find coordinates of C.

Answer 1

Dear student,

Answer: Coordinates of C can be ( 0, 5.2) or (0, -5.2)

Solution:

As we know all the sides of equilateral triangle are equal.

The length of side AB

A( -3 ,0) B ( 3, 0)

AB = √( -3-3)²+ (0-0)²

AB = √(-6)²

AB = 6 cm

So BC and AC are equal to AB.

let the coordinate of vertex C be ( 0,y) on y axis

length of AB = length of AC

A( -3 ,0) C ( 0,y)

6 = √(-3-0)²+ (0 -y)²

6 = √9+y²

take square both sides

36 = 9+ y²

y² =36-9

y² = 27

y = √27

y = 3√ 3

y= 5.196

y ≈ 5.2

so the coordinates of C are ( 0, 5.2).

The equilateral triangle can consist in III and IV quadrant too, by taking C on -y axis.

Please refer diagram attached. you will get rough estimation from that.

Hope it helps you.

Answer 2

hope this helps you...

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