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:
12.1/1
Step-by-step explanation:
Answer:
1. Either none (if you have to buy a whole pound), or 1/4 of a pound
2. 3 whole pounds or 3 and 1/4 pounds
Step-by-step explanation:
If $4 = 1 pound, then we know that $1 (which is 1/4 of $4), will let you by 1/4 pound of blueberries. Knowing this, we can simply:
Add up the one fourths
do 1/4 times $$
See how many times 4 goes into the number of dollars you have
Please correct me if I'm wrong :)
Answer:
That equation doesn't make sense, so this equation means "no solution"
Step-by-step explanation:
Answer:
x=2
Step-by-step explanation:
assuming this shape is euclidean (don't pay attention to this just some extra info, assume that all triangles on a sheet of paper have angles summing to 180)
The sum of all angles in a triangle is 180, so
90+60+15x=180
150+15x=180
15x=30
x=2
