What is the orthocenter of a triangle with corners at #(6 ,3 )#, #(4 ,5 )#, and (2 ,9 )#?
The orthocenter of triangle is
Let
Let Let
Slope of Slope of Subst. From equn. Hence, the orthocenter of triangle is
By signing up, you agree to our Terms of Service and Privacy Policy
To find the orthocenter of a triangle, you need to find the intersection point of the altitudes of the triangle. The altitude of a triangle is a line segment perpendicular to a side of the triangle, passing through the opposite vertex.
- Find the slopes of the sides of the triangle.
- Use the point-slope form to find the equations of the perpendicular bisectors of each side (these will be the altitudes).
- Find the intersection point of any two perpendicular bisectors to get the orthocenter.
For the given triangle with corners at (6, 3), (4, 5), and (2, 9):
-
The slopes of the sides are:
- Slope of side passing through (6, 3) and (4, 5) = (5-3) / (4-6) = 2/-2 = -1
- Slope of side passing through (4, 5) and (2, 9) = (9-5) / (2-4) = 4/-2 = -2
- Slope of side passing through (2, 9) and (6, 3) = (3-9) / (6-2) = -6/4 = -3/2
-
Using the point-slope form (y - y1) = m(x - x1), we find the equations of the perpendicular bisectors:
- For the side passing through (6, 3) and (4, 5), the midpoint is ((6+4)/2, (3+5)/2) = (5, 4). The slope of the perpendicular bisector is the negative reciprocal of -1, which is 1. Thus, the equation of the perpendicular bisector is y - 4 = 1(x - 5).
- Similarly, for the other sides, you'll find the equations of the perpendicular bisectors.
-
Solve any two equations of the perpendicular bisectors to find the orthocenter, which is the intersection point.
By signing up, you agree to our Terms of Service and Privacy Policy
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
- A triangle has corners A, B, and C located at #(4 ,7 )#, #(3 ,2 )#, and #(2 ,4 )#, respectively. What are the endpoints and length of the altitude going through corner C?
- A line segment is bisected by a line with the equation # -7 y + 5 x = 1 #. If one end of the line segment is at #(1 ,4 )#, where is the other end?
- What is the height of the screen?
- Describe and write an equation for the locus of points equidistant form #A(a_x, a_y) and B(b_x,b_y)#? Test what you derived for #P_A(-2,5) and P_B(6,1)? #
- What is the orthocenter of a triangle with corners at #(9 ,3 )#, #(6 ,9 )#, and (2 ,4 )#?

- 98% accuracy study help
- Covers math, physics, chemistry, biology, and more
- Step-by-step, in-depth guides
- Readily available 24/7