Answer:
(4,3)
Step-by-step explanation:
The orthocenter of a triangle is the point of intersection of the altitudes of the triangle .
The vertices are:
A(-2,5), B(6,5), and C(4,-1)
Slope of (6,5), and (4,-1) is
[tex]m = \frac{5 - - 1}{6 - 4} = 3[/tex]
Slope of altitude through A is
[tex] - \frac{1}{3} [/tex]
The equation of the altitude through A is
[tex]y - 5 = - \frac{1}{3} (x - - 2)[/tex]
[tex]y = - \frac{1}{3} x + \frac{13}{3} [/tex]
The slope of A(-2,5), B(6,5) is zero because it is a horizontal line.
The equation of altitude through (4,-1) will be the vertical line x=4.
This implies that,
[tex]y = - \frac{4}{3} + \frac{13}{3} = 3[/tex]
Hence the orthocenter is (4,3)
