<span><span><span>1. An altitude of a triangle is a line segment from a vertex perpendicular to the opposite side. Find the equations of the altitudes of the triangle with vertices (4, 5),(-4, 1) and (2, -5). Do this by solving a system of two of two of the altitude equations and showing that the intersection point also belongs to the third line. </span>
(Scroll Down for Answer!)</span><span>Answer by </span>jim_thompson5910(34047) (Show Source):You can put this solution on YOUR website!
<span>If we plot the points and connect them, we get this triangle:
Let point
A=(xA,yA)
B=(xB,yB)
C=(xC,yC)
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Let's find the equation of the segment AB
Start with the general formula
Plug in the given points
Simplify and combine like terms
So the equation of the line through AB is
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Let's find the equation of the segment BC
Start with the general formula
Plug in the given points
Simplify and combine like terms
So the equation of the line through BC is
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Let's find the equation of the segment CA
Start with the general formula
Plug in the given points
Simplify and combine like terms
So the equation of the line through CA is
So we have these equations of the lines that make up the triangle
So to find the equation of the line that is perpendicular to that goes through the point C(2,-5), simply negate and invert the slope to get
Now plug the slope and the point (2,-5) into
Solve for y and simplify
So the altitude for vertex C is
Now to find the equation of the line that is perpendicular to that goes through the point A(4,5), simply negate and invert the slope to get
Now plug the slope and the point (2,-5) into
Solve for y and simplify
So the altitude for vertex A is
Now to find the equation of the line that is perpendicular to that goes through the point B(-4,1), simply negate and invert the slope to get
Now plug the slope and the point (-4,1) into
Solve for y and simplify
So the altitude for vertex B is
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Now let's solve the system
Plug in into the first equation
Add 2x to both sides and subtract 2 from both sides
Divide both sides by 3 to isolate x
Now plug this into
So the orthocenter is (-2/3,1/3)
So if we plug in into the third equation , we get
So the orthocenter lies on the third altitude
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Answer:
B. The lower extreme increased.
Step-by-step explanation:
From the original box and whisker plot, the lower extreme (minimum) is 5 ; The upper extreme, maximum is 15.
The number of batches baked on the eight day is 20. This exceeds tbe previous maximum value. Hence, upper extreme( maximum) value of the new plot will change from 15 to 20.
The lower extreme isn't affected as the obtained value isn't below 5.
The median value will Increase and the upper quartile value will also increase. Once the upper quartile value increases, the interquartile range will also increase
6 4/5 + 6 4/5 + 2 2/3 + 2 2/3 = 18 14/15
Answer:
504
Step-by-step explanation:
We are solving for the left leaning poll
Total voters = 900 + 1100
= 2000
Number of voters who say trump was responsible = 56percent x 2000
= 1120
Number of those who say otherwise = 44% x 2000
= 880
For this network
Those who say trump is responsible = 1120 x900/2000
= 1008000/2000
= 504 registered voters
