If A(7,9),B(3,−7) and C(−3,3) represent the vertices of a triangle, then which of the following is/are correct?
A
They form an equilateral triangle.
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B
They form a right angled isosceles triangle.
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C
Orthocentre of the triangle is (−3,3)
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D
Orthocentre of the triangle is (3,−7)
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Solution
The correct options are B They form a right angled isosceles triangle. C Orthocentre of the triangle is (−3,3) Given : The vertices of triangle are A(7,9),B(3,−7) and C(−3,3) Now, finding the side lengths, AB=√42+162=4√17 units BC=√62+102=2√34 units AC=√102+62=2√34 units
As BC=AC and (AB)2=(BC)2+(AC)2, it is a right angled isosceles triangle, right angled at C. So, orthocentre =(−3,3)