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Show that the points A(3, 0), B(6, 4) and C(-1, 3) are the ver

Question

Show that the points $A (3, 0), B (6, 4)$ and $C (- 1, 3)$ are the vertices of an isosceles right triangle.

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Scarlett Discussed

Show that the points

A (3, 0), B (6, 4)

and

C (- 1, 3)

are the vertices of an isosceles right triangle.

12 mins ago

Discuss this question LIVE

12 mins ago

Text solutionVerified

Given points are

A (3, 0), B (6, 4)

and

C (- 1, 3)

A B^{2} = (x_{2} - x_{1})^{2} + (y_{2} - y_{1})^{2}

= (6 - 3)^{2} + (4 - 0)^{2} = 3^{2} + 4^{2}

= 9 + 16 = 25

B C^{2} = (- 1 - 6)^{2} + (3 - 4)^{2} = (- 7)^{2} + (- 1)^{2}

= 49 + 1 = 50

C A^{2} = (3 + 1)^{2} + (0 - 3)^{2} = 4^{2} + 3^{2}

= 16 + 9 = 25

A B^{2} = C A^{2} = 25

A B = C A

From above, two of the sides are of equal length, so triangle ABC is an isosceles triangle.

Check for: Isosceles right triangle

Sum of square of two sides

=

Square of third side

A B^{2} + A C^{2} = 25 + 25 = 50 = C B^{2}

Hence given points are vertices of an isosceles right triangle.

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Question Text	Show that the points $A (3, 0), B (6, 4)$ and $C (- 1, 3)$ are the vertices of an isosceles right triangle.
Answer Type	Text solution:1
Upvotes	150