Statement (A): The triangle formed by the points (1,1),(4,1) and (1,5) is a right angled triangle.Statement (B): The triangle formed by the points (4,5),(7,6) and (8, 9) is a scalene triangle.

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Statement (A): The triangle formed by the points $(1, 1), (4, 1)$ and $(1, 5)$ is a right angled triangle.

Statement (B): The triangle formed by the points $(4, 5), (7, 6)$ and $(8, 9)$ is a scalene triangle.

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Both A and B are true

A is false and B is true

A is true and B is false

Both A and B are false

answer is C.

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Detailed Solution

$A B = \sqrt{{(4 - 1)}^{2} + {(1 - 1)}^{2}} = 3$

$B C = \sqrt{{(1 - 4)}^{2} + {(5 - 1)}^{2}} = \sqrt{9 + 16} = 5$

$C A = \sqrt{{(1 - 1)}^{2} + {(5 - 1)}^{2}} = \sqrt{4^{2}} = 4$

ABC is right triangle

$A B = \sqrt{{(7 - 4)}^{2} + {(6 - 5)}^{2}} = \sqrt{9 + 1} = \sqrt{10}$

$B C = \sqrt{{(8 - 7)}^{2} + {(9 - 6)}^{2}} = \sqrt{1 + 9} = \sqrt{10}$

$C A = \sqrt{{(8 - 4)}^{2} + {(9 - 5)}^{2}} = \sqrt{16 + 16} = \sqrt{32}$

ABC is an isosceles triangle.

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