SOLUTION: Line l is the perpindicular bisector of AB, where A has coordinates (-2,3) and b has coordinates (5,4). Find the distance between the x and y intercepts of l.

Question 80641: Line l is the perpindicular bisector of AB, where A has coordinates (-2,3) and b has coordinates (5,4). Find the distance between the x and y intercepts of l.
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
Line l is the perpendicular bisector of AB, where A has coordinates (-2,3) and b has coordinates (5,4). Find the distance between the x and y intercepts of l.
Here is the plan of attack on this problem. First find the mid-point of line AB.
This will be the point where line 1 crosses (bisects) AB, then we will find the
the slope (m1) of AB. From that we will find the slope (m2) of the line 1. Then,
using the midpoint coordinates and m2 slope find the equation of line 1. Then,
we can find the x & y intercepts of the line. Then find the distance between them.
:
Midpoint = and
M.P (x) = =
M.P (y) = =
:
x/y coordinates: 3/2, 7/2
:
:
Find the slope (m1), of AB
:
m = = =
:
Find the slope (m2) of the perpendicular line:
We know the relationship of slopes of perpendicular lines is: m1*m2 = -1
:
(1/7) * m2 = -1
:
m2 = -7; multiplied both sides by 7
:
Find the equation of the line 1 using the point/slope formula; y-y1 = m(x-x1)
m2 = -7; y1 = 7/2; x1 = 3/2
:
y - (7/2) = -7(x - (3/2))
y - (7/2) = -7x + (21/2)
y = -7x + (21/2) + (7/2)
y = -7x + 28/2
y = -7x + 14
:
We know the y intercept (x=0) will be 14
:
Find the x intercept (y=0)
-7x + 14 = 0
-7x = -14
x = -14/-7
x = +2
:
WE can find the distance between the intercepts using pythag: a^2 + b^2 = c^2
Distance will be c:
:
c = Sqrt(2^2 + 14^2)
c = Sqrt(4 + 196)
c = Sqrt(200)
c = 14.142 is the distance between the intercepts

Did this all makes sense to you,
Hope you did not get lost in the "Heat of Battle!"?

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