Question

3. Two of the vertices of an equilateral triangle are (0, -a)

Answer 1

The third coordinate of the equilateral triangle is $(\sqrt3a,0)$. Ir can be obtained by distance formula.

What is distance formula?

It gives the distance between two coordinates.

Distance formula is given by the following expression:

$\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

Consider the third cordinate is (x,0) and x is positive because it is on tight side on the x axis.

Now, since the triangle is equilateral hence, the distance of (x,0) from (0, -a) and (0, a) should be equal to distance between (0, -a) and (0, a).

Now, caculate the distance between (0,-a) and (0, a).$\sqrt{(0-0)^2+(-a-a)^2}=2a$

Now, distance between (x,0) and (0, a) should be 2a.

$\sqrt{(x-0)^2+(0-a)^2}=2a\\\sqrt{x^2+a^2}=2a$

Now, square on both the sides.

$x^2+a^2=4a^2\\x^2=3a^2\\x=\sqrt3a$and $-\sqrt3a$

But the negative value of x is not possible because the coordinate lies on the right side.

Hence, the third coordinate of equilateral triangle is $(\sqrt3a,0)$.

Learn more about distance formula from the following link:

brainly.com/question/7243416

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