Question

find the orthocenter of \\( \triangle a b c \\).
\\( a(0,0), b(7,0), c(7,2) \\)

the orthocenter is \\( \square \\)
(type an ordered pair)

Explanation:

Step1: Analyze the triangle type

Since \(A(0,0)\), \(B(7,0)\), \(C(7,2)\), \(AB\) is a horizontal line (\(y = 0\)) and \(BC\) is a vertical line (\(x=7\)).

Step2: Recall the property of right - angled triangle orthocenter

For a right - angled triangle, the orthocenter is the vertex of the right angle.
Since \(AB\perp BC\) (because a horizontal line \(AB\) and a vertical line \(BC\) are perpendicular), the right - angle vertex is \(B\).

Answer:

\((7,0)\)