Question

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

Answer 1

(1,6)

Explanation:

you can see on the diagram that the point (1,6) is at the middle, which is the orthocenter

Answer 2

(1,6)

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:
`√((x_2-x_1)^2+(y_2-y_1)^2)`

Using distance formula

`AB=(1-1)^2+(6-2)^2=16`

`BC=(5-1)^2+(6-6)^2=16`

`AC^2=(1-5)^2+(2-6)^2=32`

`AC^2=AB^2+BC^2`

Hence, the triangle is a right triangle because it satisfied Pythagoras theorem

`(Hypotenuse)^2=(Base)^2+(Perpendicular\;side)^2`

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).