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mina [271]
3 years ago
6

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

Mathematics
2 answers:
iren2701 [21]3 years ago
6 0
(1,6)
This should help for future problems
<span>https://www.mathportal.org/calculators/analytic-geometry/triangle-calculator.php</span>
salantis [7]3 years ago
6 0

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: \sqrt{(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).

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