Check whether (5, – 2), (6, 4) and (7, – 2) are the vertices of an isosceles triangle.

Solution

Let the given points be A(5, -2), B(6, 4) and C(7, -2). Then

AB space equals space square root of open parentheses 6 minus 5 close parentheses squared plus left curly bracket 4 minus left parenthesis negative 2 right parenthesis right curly bracket squared end root space space space space space equals space square root of open parentheses 1 close parentheses squared plus left parenthesis 6 right parenthesis squared end root equals square root of 1 plus 36 end root space space space space space equals square root of 37 BC space equals space square root of open parentheses 7 minus 6 close parentheses squared plus left parenthesis negative 2 minus 4 right parenthesis squared end root space space space space space space equals space square root of open parentheses 1 close parentheses squared plus left parenthesis negative 6 right parenthesis squared end root space space space space space space space equals space square root of 1 plus 36 end root equals 37

Since AB = BC
Therefore, ABC is an isosceles triangle.

Some More Questions From Introduction to Trigonometry Chapter

For Daily Free Study Material Join wiredfaculty