A line segment is bisected by a line with the equation # -3 y + x = 1 #. If one end of the line segment is at #(1 ,6 )#, where is the other end?

Answer 1

The other end is a #(4.6, -4.8)#

Put the bisector's equation in slope-intercept form:

#y = 1/3x - 1/3# #[1]#
The slope is, #m = 1/3#
The slope, n, for the bisected line is, #n = -1/m = -1/(1/3) = -3#
Use the slope and the point, #(1, 6)# into the slope, #-3#, into the slope-intercept form of a line and then solve for b:
#6 = -3(1) + b#
#b = 9#

The bisected line's equation is as follows:

#y = -3x + 9# #[2]#
Subtract equation #[2]# from equation #[1]#
#y - y= 1/3x + 3x - 1/3 - 9#
#0 = 10/3x - 28/3#

The point of intersection's x coordinate is:

#x = 2.8#

The x coordinate increased by 1.8 to go from 1 to 2.8; hence, to reach the other end of the line, the x coordinate must increase by twice that amount, or 3.6.

#x = 1 + 3.6 = 4.6 #

The other end of the line's x coordinate is this.

To find the y coordinate, substitute 4.6 for x into equation #[2]#

#y = -3(4.6) + 9

#y = -4.8#
Sign up to view the whole answer

By signing up, you agree to our Terms of Service and Privacy Policy

Sign up with email
Answer 2

To find the other end of the line segment bisected by the line ( -3y + x = 1 ), given one end at (1, 6), we can solve for the intersection point of the line and the segment. We find the coordinates of the other end by reflecting the given point across the line.

Sign up to view the whole answer

By signing up, you agree to our Terms of Service and Privacy Policy

Sign up with email
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.

Not the question you need?

Drag image here or click to upload

Or press Ctrl + V to paste
Answer Background
HIX Tutor
Solve ANY homework problem with a smart AI
  • 98% accuracy study help
  • Covers math, physics, chemistry, biology, and more
  • Step-by-step, in-depth guides
  • Readily available 24/7