Question

Find the orthocenter of △ABC. A(2, 3), B(−4, −3), C(2, −3)

Answer 1

ANSWER

$\boxed { A. \: \: (2,-3) }$

EXPLANATION.

The orthocenter is the point of intersection of any two altitudes of the triangle.

First, you need to determine the slope of each side of the triangle.

△ABC has vertices A(2, 3), B(−4, −3), C(2, −3).

$slope \: of \: AB = \frac{3 - - 3}{2 - - 4} = \frac{6}{6} = 1$

$slope \: of \: AC = \frac{ 3 - - 3}{2 - 2} = \frac{6}{0}$

This line has undefined slope, which means it is a vertical line.

$slope \: of \: BC = \frac{ - 3 - - 3}{ 2 - - 4} = \frac{0}{6} = 0$

The slope of this line is zero, meaning the line is a horizontal line.

This implies that side BC and side AC of the given triangle are perpendicular and will intersect at C since they are the altitudes of triangle ABC.

Hence the orthocentre is

$(2,-3)$

See diagram in attachment.