Question

ABC is an equilateral triangle whose vertex A has the co-ordinates (0, √3). Find the co- ordinates of B and C. ​

Answer 1

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:

• B = (-1, 0)
• C = (1, 0)

Learn more about the 30-60-90 triangle here:

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