ANSWER
[tex] \boxed { A. \: \: (2,-3) }[/tex]
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).
[tex]slope \: of \: AB = \frac{3 - - 3}{2 - - 4} = \frac{6}{6} = 1[/tex]
[tex]slope \: of \: AC = \frac{ 3 - - 3}{2 - 2} = \frac{6}{0} [/tex]
This line has undefined slope, which means it is a vertical line.
[tex]slope \: of \: BC = \frac{ - 3 - - 3}{ 2 - - 4} = \frac{0}{6} = 0[/tex]
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
[tex](2,-3)[/tex]
See diagram in attachment.
