5-2 Medians and Altitudes of Triangles
4. COORDINATE GEOMETRY Find the coordinates of the orthocenter of triangle ABC with vertices A(–3, 3), B
(–1, 7), and C(3, 3).
SOLUTION:
The slope of
is
. So, the slope of the altitude, which is perpendicular to
the equation of the altitude from C to
is
. Now,
is:
Use the same method to find the equation of the altitude from A to
.That is,
Solve the equations to find the intersection point of the altitudes.
So, the coordinates of the orthocenter of
is (–1, 5).
COORDINATE GEOMETRY Find the coordinates of the orthocenter of each triangle with the given
14.
–
–
SOLUTION:
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is
or
Page 1
So, the slope of the altitude, which is perpendicular to
is
Now, the
5-2 Medians and Altitudes of Triangles
COORDINATE GEOMETRY Find the coordinates of the orthocenter of each triangle with the given
vertices.
14. J(3, –2), K(5, 6), L(9, –2)
SOLUTION:
The slope of
is
or
equation of the altitude from L to
So, the slope of the altitude, which is perpendicular to
is
Now, the
is:
Use the same method to find the equation of the altitude from J to
.That is,
Solve the equations to find the intersection point of the altitudes.
So, the coordinates of the orthocenter of
is (5, –1).
15. R(–4, 8), S(–1, 5), T(5, 5)
SOLUTION:
is
or –
is 1. Now, the
is:
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5-2 Medians and Altitudes of Triangles
15. R(–4, 8), S(–1, 5), T(5, 5)
SOLUTION:
The slope of
is
or –1. So, the slope of the altitude, which is perpendicular to
equation of the altitude from T to
is 1. Now, the
is:
Use the same way to find the equation of the altitude from R to
.That is,
Solve the equations to find the intersection point of the altitudes.
So, the coordinates of the orthocenter of
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is (–4, –4).
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