Question

A(2,2), B(-2,4), C(2,6) are the vertices of a triangle ABC. show that ABC is an isosceles triangle.

Answer 1

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Answer 2

Triangle

Given:

The coordinates of point A, B and C are given as (2,2), (2,4), (2,6) respectively.

ABC forms a triangle.

To find:

Prove ABC is an isosceles triangle.

Explanation:

Isosceles triangle: A triangle is said to be an isosceles triangle if length of any two sides and measure of two angles are equal.

To prove,

ABC is an isosceles triangle.

Length between 2 points coordinate points can be found out by,

$d=\sqrt{(x_{2}- x_{1})^2+ (y_{2}-y_1)^2 }\\\\where \ x_1, x_2, y_1, y_2 \ are \ the \ coordinates \ of \ the \ two\ points.$

So, length AB will be ,

$AB=\sqrt{(-2-2)^2+(4-2)^2}=\sqrt{16+4}=\sqrt{20}=2\sqrt{5}\ units.\\\\BC= \sqrt{(2-(-2))^2+(6-4)^2}=\sqrt{16+4}=\sqrt{20}=2\sqrt{5}\ units.\\\\AC=\sqrt{(2-2)^2+(6-2)^2}=\sqrt{0+16}=\sqrt{16}=4\ units.$

We can see that length of AB  and BC is same and that of AC is different.

Hence, ΔABC is an isosceles triangle.