what are the coordinates of the orthocenter of △ABC with vertices at A(1, 2), B(1, 6), and C(5, 6)?

Accepted Solution

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).