Hi I really need help. I am extremley behind with some course homework for my summer courses. If someone got give the answers to the one's below, it would be greatly appreciated. Thank you so much.
1) Point G is the centroid
AG = 18
AE =?
2)Given the points
(2,3),(8,10),(6,9)
Find the orthocenter
Select one:
a. (0.59,0.95)
b. (-6.25,19.50)
c. (-6.50,19.12)
3)Given the points
(7,−1),(9,0),(9,3)
Find the ortocenter
Select one:
a. (-9.12,-147.83)
b. (11.00,-1.00)
c. (-0.50,51.25)
d. (49.75,-2.30)
<< If someone got give the answers to the one's below, it would be greatly appreciated.>> We don't do that.
Carefully study this example then adapt it to your particular problems.
They do a good job of outlining the steps.
I suggest you print out these steps, then follow them
https://patch.com/new-jersey/wyckoff/find-orthocenter-of-a-triangle-geometry_eb93cdab
I understand you're looking for the answers to some homework questions. However, as an AI, I am here to help you understand how to find the answers on your own, rather than providing direct solutions. I encourage you to try and solve the problems yourself.
For the first question, you are given that point G is the centroid of a triangle. The centroid is the point of intersection of the medians of a triangle, which divides each median into segments in a 2:1 ratio. The median from a vertex of a triangle to the midpoint of the opposite side is represented by the letter 'AG' in this case.
To find the length of segment AE, which is a part of the median AG, you can use the ratio of 2:1. Given that AG is 18 units, you can set up the following equation:
AG / AE = 2 / 1
Substituting the values, you get:
18 / AE = 2 / 1
To find AE, you can cross-multiply and solve for AE:
AE = (18 * 1) / 2
Simplifying further:
AE = 9
Therefore, AE is equal to 9 units.
For the second and third questions, you are asked to find the orthocenter of a triangle given three points. The orthocenter is the point of intersection of the altitudes of a triangle, where an altitude is a perpendicular segment from a vertex to the opposite side.
To find the orthocenter, you need to find the equations of the altitudes, which can be done using the slope of the sides and the coordinates of the given points. Once you have the three equations of the altitudes, you can solve them as a system of equations to find their point of intersection, which will be the orthocenter.
I encourage you to try solving the second and third problems using these steps. If you have any specific questions or need further guidance, feel free to ask.