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Question 389531: Please help me. I missed a week of school and I am so lost. I have this take home test that is due soon.
So, the first problem is to write an equation of the perpendicular bisextor of the line segment whose endpoints are (-1. 1) and (7, 5) and there is also a grid provided for me but it is optional. Can you please explain this step by step so I could understand other math material. Thank you!
Found 2 solutions by haileytucki, lwsshak3:
Answer by haileytucki(390)   (Show Source):
You can put this solution on YOUR website! I may be mistaken, but your fist set said -1.1, I assumed it was -1, 1.
Hope this helps:
(-1,1),(7,5)
Use y=mx+b to calculate the equation of the line, where m represents the slope and b represents the y-intercept.
To calculate the equation of the line, use the y=mx+b format.
Slope is equal to the change in y over the change in x, or 'rise over run'.
m=(change in y)/(change in x)
The change in x is equal to the difference in x-coordinates (also called run), and the change in y is equal to the difference in y-coordinates (also called rise).
m=(y2-y1)/(x2-x1)
Substitute in the values of x and y into the equation to find the slope.
m=(5-(1))/(7-(-1))
Multiply -1 by each term inside the parentheses.
m=(5-(1))/(7+1)
Add 1 to 7 to get 8.
m=(5-(1))/(8)
Multiply -1 by each term inside the parentheses.
m=(5-1)/(8)
Subtract 1 from 5 to get 4.
m=(4)/(8)
Reduce the expression (4)/(8) by removing a factor of 4 from the numerator and denominator.
m=(1)/(2)
Find the value of b using the formula for the equation of a line.
y=mx+b
Substitute the value of m into the equation.
y=((1)/(2))*x+b
Substitute the value of x into the equation.
y=((1)/(2))*(-1)+b
Substitute the value of y into the equation.
(1)=((1)/(2))*(-1)+b
Since b is on the right-hand side of the equation, switch the sides so it is on the left-hand side of the equation.
((1)/(2))*(-1)+b=(1)
Multiply ((1)/(2)) by (-1) to get ((1)/(2))(-1).
((1)/(2))(-1)+b=(1)
Remove the parentheses around the expression 1.
((1)/(2))(-1)+b=1
Multiply (1)/(2) by -1 to get -(1)/(2).
(-(1)/(2))+b=1
Reorder the polynomial -(1)/(2)+b alphabetically from left to right, starting with the highest order term.
b-(1)/(2)=1
Find the value of b.
b=(3)/(2)
Now that the values of m(slope) and b(y-intercept) are known, substitute them into y=mx+b to find the equation of the line.
y=(x)/(2)+(3)/(2)
Answer by lwsshak3(11628)  (Show Source):
You can put this solution on YOUR website! 1. First find the slope of the line segment then find the midpoint of the line segment
Using the coordinates of the two end points, (-1,1) and (7,5),
slope =∆y/∆x =(1-5)/(-1-7)=-4/-8 =1/2
midpoint = (x1+x2)/2,(y1+y2)/2=(-1+7)/2,(1+5)/2=(3,3)
slope of perpendicular bisector = negative reciprocal or line segment = -2
using this slope, the coordinates of the midpoint (3,3), and the point slope formula,y=mx+b
3=-2*3+b
b=3+6=9
equation then becomes, y=-2x +9
ans: the equation of the perpendicular bisector of a line segment whose endpoints are (-1,1) and (7,5)
is y=-2x+9
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