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  • Verify the following: (i) (0, 7, 10), (- 1, 6, 6) and (- 4, 9, 6) are the vertices of an isosceles triangle.

3. (ii) Verify the following:

(0, 7, 10), (- 1, 6,  6) and (- 4, 9,  6) are the vertices of right angled triangle.

Answers (1)

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Given three points, A = (0, 7, 10), B = (-1, 6, 6) and C = (-4, 9, 6)

The distance between two points (x_1,y_1,z_1) and (x_2,y_2,z_2) is given by

d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2+(z_2-z_1)^2}

The distance AB

AB=\sqrt{(-1-0)^2+(6-7)^2+(6-10)^2}

AB=\sqrt{1+1+16}

AB=\sqrt{18}

The distance BC

BC=\sqrt{(-4-(-1))^2+(9-6)^2+(6-6)^2}

BC=\sqrt{9+9+0}

BC=\sqrt{18}

The distance CA 

CA=\sqrt{(-4-0)^2+(9-7)^2+(6-10)^2}

CA=\sqrt{16+4+16}

CA=\sqrt{36}

CA=6

As we can see, 

(AB)^2+(BC)^2=18+18=36=(CA)^2

Since this follows the Pythagoras theorem, we can say that ABC is a right-angled triangle.

Posted by

Pankaj Sanodiya

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