Question

An equilateral triangle ABC is such that the side BC is parallel to X-axis. Then the slopes of its sides AB, BC, CA respectively are

• A. \(\sqrt{3},0,-\sqrt{3}\)
• B. \(\sqrt{3},\sqrt{3},\sqrt{3}\)
• C. 1, 0, -1
• D. \(\sqrt{3},0,\sqrt{3}\)

Answer 1

The Correct Option is A

Let the coordinates of points \( B \), \( C \), and \( A \) be \( B(x_1, y_1) \), \( C(x_2, y_2) \), and \( A(x_3, y_3) \) respectively. Since BC is parallel to the X-axis, the slope of BC is \( 0 \).
In an equilateral triangle, the lengths of all sides are equal. Using geometric properties and calculating the slopes of the sides AB, BC, and CA:

1. The slope of BC is \( 0 \), as BC is parallel to the X-axis.
2. The slopes of AB and CA are the slopes of the other two sides of the triangle.

Since the triangle is equilateral, the slopes of these sides are equal in magnitude but opposite in sign, resulting in slopes of \( \sqrt{3} \) and \( -\sqrt{3} \).

The correct answer is option (A):\(\sqrt{3},0,-\sqrt{3}\)