Answer:
B = (-1, 0)
C = (1, 0)
Step-by-step explanation:
Properties of an Equilateral Triangle
- Three sides of equal length
- All interior angles are 60°
Given:
- ΔABC is an equilateral triangle
- Vertex A is at (0, √3)
Drawing an altitude from vertex A divides the triangle into two 30-60-90 triangles.
A 30-60-90 triangle is special right-angled triangle where:
- Angles are in the ratio 1 : 2 : 3
- Sides are in the ratio 1 : √3 : 2
Therefore, the formula for the sides is: b : b√3 : 2b, where:
- b = shortest side opposite the 30° angle
- b√3 = side opposite the 60° angle
- 2b = longest side (hypotenuse) is opposite the right angle
As Vertex A has the co-ordinates (0, √3), the side opposite the 60° angle is √3 units.
Using the ratios to find b (shortest side length):
b√3 = √3 ⇒ b = 1
As the altitude divides BC into two equal line segments, and the length of the shortest side of the right triangles is 1 unit, the coordinates of B are C are:
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