Question 831458: Please help me solve this : Line JK has endpoints J(4,6) and K(0,2). The intersection of Line JK and its perpendicular bisector is (2,4) . Write the equation for the perpendicular bisector of line JK.
Answer by hovuquocan1997(83)   (Show Source):
You can put this solution on YOUR website! First, because you have 3 points for line JK, which is (4,6), (0,2) you should start finding the equation for this line first in order to find the perpendicular line. A linear equation has a formula like this y=ax + b
Create a system of two equations:
First: 6=4a+b
Second: 2=0a+b
So you have system of 2 equations:
Then you can find a=1 and b=2
So the equation would be : y=1x + 2 which is y = x + 2
Now let's find the perpendicular line. it also has the equation form like this
Y = ax + b
But in order to be perpendicular with JK, the a in this equation and the a in JK equation must multiply together and give you -1
so 1.a = -1 ===> a = -1
So you have y = -x + b
Now you have point (2,4) given on the line in the question. PLUG IT IN
4 = -(2) + b
b = 6
TA-DAH. You have the equation y = -x + 6 :D
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