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Show that the points A(7, 10), B(-2, 5) and C(3, -4) are the v

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Show that the points $A (7, 10), B (- 2, 5)$ and $C (3, - 4)$ are the vertices of an isosceles right triangle.

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Show that the points

A (7, 10), B (- 2, 5)

and

C (3, - 4)

are the vertices of an isosceles right triangle.

11 mins ago

Discuss this question LIVE

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Text solutionVerified

Given points are

A (7, 10), B (- 2, 5)

and

C (3, - 4)

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

= (- 2 - 7)^{2} + (5 - 10)^{2} = (- 9)^{2} + (- 5)^{2}

= 81 + 25 = 106

B C^{2} = (3 + 2)^{2} + (- 4 - 5)^{2} = (5)^{2} + (- 9)^{2}

= 25 + 81 = 106

C A^{2} = (7 - 3)^{2} + (10 + 4)^{2} = (4)^{2} + (14)^{2}

= 16 + 196 = 212

A B^{2} + B C^{2} = 106

\Rightarrow A B = BC

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} + B C^{2} = 106 + 106 = 212 = C A^{2}

Hence given points are vertices of an isosceles right triangle.

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Question Text	Show that the points $A (7, 10), B (- 2, 5)$ and $C (3, - 4)$ are the vertices of an isosceles right triangle.
Answer Type	Text solution:1
Upvotes	150

Show that the points A(7,10),B(−2,5) and C(3,−4) are the vertices of an isosceles right triangle.

Text solutionVerified

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Show that the points $A (7, 10), B (- 2, 5)$ and $C (3, - 4)$ are the vertices of an isosceles right triangle.