A line segment is bisected by a line with the equation 5 y + 2 x = 1 . If one end of the line segment is at (3 ,4 ), where is the other end?

1 Answer
Leland Adriano Alejandro
Oct 7, 2017

the other is end is at (-13/29, -134/29)

Explanation:

The given line is 5y+2x=1
The line perpendicular to this line and passing thru point U(3, 4) is
y-4=(5/2)(x-3) by the two-point form
or 5x-2y=7
Simultaneous solution of
2x+5y=1 and 5x-2y=7 yields point I(37/29, -9/29)

Let v=vertical distance from point I(37/29, -9/29) to U(3, 4)
v=4--9/29=125/29
Let h=horizontal distance from point I(37/29, -9/29) to U(3, 4)
h=3-37/29=50/29
Let the other end point be D(x_o, y_o)

x_o=37/29-h=37/29-50/29= -13/29
y_o=-9/29-125/29=-134/29

Check by distance formula from point I(37/29, -9/29) to U(3, 4)
d_1=sqrt((3-37/29)^2+(4--9/29)^2)=(25sqrt(29))/29

Check by distance formula from point I(37/29, -9/29) to D(-13/29, -134/29)
d_2=sqrt((37/29--13/29)^2+(-9/29--134/29)^2)=(25sqrt(29))/29

Therefore d_1=d_2

God bless....I hope the explanation is useful.

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