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Question

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=417 units
BC=62+102=234 units
AC=102+62=234 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)

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