Question

Show that the points:
i) (2, 4), (2, 6), (2 + √3, 5) form an equilateral triangle.
ii) (1, 3), (3, -1), (-5, -5) form a right angled triangle.
iii) (-2, 5), (3, -4), (7, 10) form a right angled isosceles triangle.
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Answer 1

(i) Let A(2,4), B(2,6) and C(2+√3, 5) be the vertices of an equilateral triangle.

Now,

Let us assume that the triangle ABC is equilateral.

Thus, AB = BC = CA

Now, using distance formula,

AB

= √(2-2)²+(6-4)²

= √4

=2

BC

= √(2+√3 -2)² + (5-6)²

= √3 + 1

= √4

= 2

CA

= √(2 - 2 - √3)² + (4-5)²

= √3 + 1

= √4

= 2

Thus, AB, BC and CA are equal, so the given triangle is equilateral,


Do (ii) and three with the same process.

Answer 2

Answer:

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