Answer:
(1,6)
Step-by-step explanation:
We are given that the vertices of triangle ABC are A at (1,2),B at (1,6) and C at (5,6).
We have to find the coordinates of the orthocenter.
Distance formula: [tex]\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
Using distance formula
[tex]AB=(1-1)^2+(6-2)^2=16[/tex]
[tex]BC=(5-1)^2+(6-6)^2=16[/tex]
[tex]AC^2=(1-5)^2+(2-6)^2=32 [/tex]
[tex]AC^2=AB^2+BC^2[/tex]
Hence, the triangle is a right triangle because it satisfied Pythagoras theorem
[tex](Hypotenuse)^2=(Base)^2+(Perpendicular\;side)^2[/tex]
The orthocenter is the intersection of three altitudes of triangle .The orthocenter of right triangle is the vertex of triangle .
The vertex of triangle is at B.
Therefore, the ortho-center of triangle ABC is B(1,6).
