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vova2212 [387]
1 year ago
13

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

Mathematics
1 answer:
s344n2d4d5 [400]1 year ago
8 0

Answer:

B = (-1, 0)

C = (1, 0)

Step-by-step explanation:

<u>Properties of an Equilateral Triangle</u>

  • Three sides of <u>equal length</u>
  • All interior angles are 60°

<u>Given</u>:

  • 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 <u>special right-angled triangle</u> 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 <u>side opposite the 60° angle</u> 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:

brainly.com/question/27942542

brainly.com/question/27976403

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