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DedPeter [7]
1 year ago
9

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

Mathematics
1 answer:
egoroff_w [7]1 year ago
5 0

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=\sqrt3aand -\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

#SPJ1

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