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?

Answer 1

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

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#

May God bless you all. I hope this explanation helps.

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Answer 2

To find the other end of the line segment bisected by the line (5y + 2x = 1), given that one end is at (3, 4), you first find the equation of the line segment. Then, you solve the system of equations formed by the given line and the line segment's equation to find their point of intersection, which represents the other end of the line segment.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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