Question

Can anyone solve this 35th question and give me clear explanation.dont give wrong answer pls

Answer 1

Answer:

answer will be c)

Step-by-step explanation:

because when point on x axis is 0 then only it can become an equilateral triangle

so point on x axis is 0 and so the option c

Answer 2

Answer:

c) (0, 2 - 3√3). Please mark me as brainliest.

Step-by-step explanation:

Here, y-axis passes through the centre of the line from the points (3,2) and (-3,2). [As y value is same, x value is additive inverse)

So, the third point will lie somewhere at x = 0. (As y-axis passes through the centre of the line from the points (3,2) and (-3,2), and in equilateral triangle, perpendicular bisector of a side passes through opposite point)

Also, y will be negative, as the triangle includes origin.

Now, we will use distance formula:

(Sides in equilateral triangle are equal)

$\sqrt{(3 - (-3))^2 + (2 - 2)^2} = \sqrt{(3 - 0)^2 + (2 - y)^2 } \\\sqrt{36 + 0} = \sqrt{9+ 4 + y^2 - 4y}\\\sqrt{36} = \sqrt{y^2 - 4y + 13}\\y^2 - 4y + 13 = 36\\y^2 - 4y - 23 = 0$

Now we will use quadratic fromula:

$y_1 = \frac{-(-4) + \sqrt{(-4)^2 - 4(1)(-23)}}{2(1)} \\y_1 = \frac{4 + \sqrt{16 + 92}}{2} \\y_1 = \frac{4 + \sqrt{108}}{2} \\y_1 = \frac{4 + 6\sqrt{3}}{2}\\y_1 = 2 + 3\sqrt{3}\\y_2 = \frac{-(-4) - \sqrt{(-4)^2 - 4(1)(-23)}}{2(1)} \\y_2 = \frac{4 - \sqrt{16 + 92}}{2} \\y_2 = \frac{4 - \sqrt{108}}{2} \\y_2 = \frac{4 - 6\sqrt{3}}{2}\\y_2 = 2 - 3\sqrt{3}$

So, y = 2 + 3√3 or 2 - 3√3.

But, only 2 - 3√3 is negative.

So, (0, 2 - 3√3)