Find an equation for the perpendicular bisector of the line segment whose endpoints
are (5, -4) and (-9, -8)
Answer:
y= -7/2x-26/2 or y= -7/2x-13
Explanation:
To solve this question you need all of these formulas:
gradient: [tex]\frac{y2-y1}{x2-x1}[/tex] , Point-Slope [tex]y-y1=m(x-x1)[/tex] ,
perpendicular m [tex](m1)x(m2)=-1[/tex] , Midpoint [tex](\frac{x1+x2}{2}[/tex],[tex]\frac{y1+y2}{2} )[/tex]
and equation of a line [tex]y=mx+c[/tex]
where m stands for gradient
First things first.
To start you have to know the data of the line that includes the two endpoints, so you calculate its gradient (m) of this line with the gradient fromula: [tex]m=\frac{-4-(-8)}{5-(-9)}[/tex] , which equals 4/14 or 2/7
(It can also be called rise/run) (Remember the rule of signs where - and - equal +)
with that information you can proceed with the point-slope or point-gradient formula, so you plug the values: y-(-8) = 2/7 (x-(-9)), which results in y+8=2/7(x+9) and then y+8=2/7x+18/7.
To finish the equation you move eight to the other side. To simplify things you can change it into a fraction as I did, and remember to change signs.
y=2/7x+18/7 -8 -> y=2/7x+18/7-56/7 . This gives us the number of y=2/7x-38/7, which is the equation of the first line.
Now to know the gradient of the second line you apply the formula of perpendicular bisector where m1 x m2 = -1. We know m1 (gradient of the first line) is 2/7, so m2 = [tex]\frac{-1}{2/7}[/tex] = -7/2. m2 is therefore -7/2
Now you have to know the midpoint between the two endpoints, which will act as the start point of the perpendicular bisector
M (midpoint) = [tex](\frac{-9+5}{2} ,[/tex][tex]\frac{8+(-4)}{2} )[/tex], which give us the coordinates of (-2, -6)
(remember, x coordinate is always first)
with this point we can apply again the point-slope formula to know the equation of the line:
y-(-6)=-7/2(x-(-2)) -> y+6=-7/2(x+2) -> y+6=-7/2x - 14/2
Move the 6 to isolate the y
y=-7/2x -14/2 - 12/2
which equals y= -7/2x -26/2
You can check the results in this page: GraphPlotter
https://www.transum.org/Maths/Activity/Graph/Desmos.asp
To make sure the answer is correct.
Hope it helps :)
CAN SOMEONE PLEASE HELP I WILL GIVE 30 POINTS AND MARK BRAINLIEST IF THE ANSWER IS CORRECT ALSO NO LINKS PLEASE
Answer:
the least developed countries tend have the highest agricultural populatian densities A.true B.false the answer is A.true
Explanation:
sorry for wrong
Explain why Pakistan steel mills is an industry in the formal sector
Answer:
The Pakistan Steel Mills Corporation,colloquially referred to as Pak Steels, is a Pakistan-based company that produces long-rolled steel and heavy metal products in the country.
Explanation:
belize and costa rica are two countries in ____
A. North America
B. South America
C. the Caribbean
D. Central America
plz and ty
Answer:
they are both in Central America
Greenhouse Gases Worksheet
help me pls
Answer:
1.)second page
1. CO2
2. Million
3. increase
4. human activities
5. deforestation
6. fuels
7. oil
8. oxygen
9. deforestation
10. increase
11. 2050
2.) sorry I'm out of time I can't answer this part sorry :( this is page 2
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
3.)
1.chemicals
2.Radiation
3.increasing
4.trapping
which ocean keeps southeast asia and india soaked with monsoons for months on end
Answer:
Indian Ocean
Explanation: