The orthocenter is the point where the three altitudes meet.
sketch the graph and you will see that AB is a horizontal line, the altitude is a vertical line through the point (1,3), so the equation of this altitude is x=1
next, find another altitude. I'll use the altitude of BC.
the slope of BC is (6-3)/(4-1)=1, so the slope of the altitude, which is perpendicular to BC going through the point A (0,6), is -1, the equation of the altitude of BC is y=-x+6
the system of equation : x=1
y=-x+6
has a solution (1, 5)
the solution is where the two lines meet, the meeting point is the orthocenter.
Double check by find the equation for other altitude:
slope of AC: (3-6)/(1-0)=-3
slope of altitude of AC: 1/3
equation of altitude of AC: y=(1/3)x+b
the altitude of AC goes through point B (4,6), so we can find out b by plug x=4, y=6 in the equation: 6=(1/3)*4+b, b=14/3
y=(1/3)x+14/3
Is (1,5) also a solution to this equation? Plug x=1 in the equation, we get y=5, so yes, (1,5) is a point on the third altitude.
Answer:
Step-by-step explanation:
H(3,2) & J(4, 1)

K(-2,-4) & M(-1 , -5)
![Slope =\dfrac{-5-[-4]}{-1-[-2]}\\\\=\dfrac{-5+4}{-1+2}\\\\= \dfrac{-1}{1}\\\\\\= -1](https://tex.z-dn.net/?f=Slope%20%3D%5Cdfrac%7B-5-%5B-4%5D%7D%7B-1-%5B-2%5D%7D%5C%5C%5C%5C%3D%5Cdfrac%7B-5%2B4%7D%7B-1%2B2%7D%5C%5C%5C%5C%3D%20%5Cdfrac%7B-1%7D%7B1%7D%5C%5C%5C%5C%5C%5C%3D%20-1)
Line HJ and KM have same slopes. So, they are parallel
Answer:
- 8 and 4: A
- 8 and 6: C
- 8 and 10: B
Step-by-step explanation:
<u>8 and 4:</u>
Multiples of 8: 8, 16, 24
Multiples of 4: 4, 8, 12, 16
<u>8 and 6:</u>
Multiples of 8: 8, 16, 24
Multiples of 6: 6, 12, 18, 24
<u>8</u><u> </u><u>and</u><u> </u><u>10</u><u>:</u>
Multiples of 8: 8, 16, 24, 32, 40
Multiples of 10: 10, 20, 30, 40
Student b? could you send a full picture
Using proportions, it is found that the ordered pair that represents the location of the layover is given by: (2.75, 1.5).
<h3>What is a proportion?</h3>
A proportion is a fraction of a total amount, and the measures are related using a rule of three.
In this problem, the flight distance is partitioned in a ratio of 3:1, hence:
L - Nv = 3/4(Ny - Nv).
This ratio is applied for both coordinates, hence, for the x-coordinate:



x = 2.75.
For the y-coordinate:


x = 1.5.
More can be learned about proportions at brainly.com/question/24372153
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