# A line segment is bisected by a line with the equation # - 3 y + 2 x = 2 #. If one end of the line segment is at #( 7 , 9 )#, where is the other end?

(151/13,27/13)

Rewrite the equation of the bisector in the form

Therefore its gradient equals to

Since the gradient product of two perpendicular lines is

Solve for the equation of the line segment (which includes the point

Solve for the

Now you can find the

Solve for the

Therefore coordinate for the other end point is

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

To find the coordinates of the other end of the line segment, we need to determine the point where the given line bisects it. First, we need to find the slope of the given line by rearranging the equation into slope-intercept form, which is (y = mx + b), where (m) is the slope and (b) is the y-intercept.

Given equation: (-3y + 2x = 2)

Rearranging the equation:

(-3y = -2x + 2)

(y = \frac{-2x + 2}{-3})

(y = \frac{2}{3}x - \frac{2}{3})

So, the slope of the given line is (m = \frac{2}{3}).

Since the line bisects the segment, its slope should be perpendicular to the line segment. Therefore, the slope of the line bisecting the segment is the negative reciprocal of (\frac{2}{3}), which is (-\frac{3}{2}).

Now, we use the midpoint formula to find the coordinates of the other end of the line segment. Let ((x_1, y_1)) be the given endpoint, which is ((7, 9)), and ((x_2, y_2)) be the coordinates of the other end.

Midpoint formula:

[x_2 = \frac{x_1 + x_2}{2}] [y_2 = \frac{y_1 + y_2}{2}]

Substituting the given endpoint and the slope of the line bisecting the segment into the midpoint formula, we get:

[x_2 = \frac{7 + x_2}{2}] [y_2 = \frac{9 + y_2}{2}]

Solving these equations simultaneously, we find the coordinates of the other end of the line segment:

[x_2 = 7] [y_2 = 6]

So, the other end of the line segment is at ((7, 6)).

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

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.

- Let #A(x_a,y_a)# and #B(x_b,y_b)# be two points in the plane and let #P(x,y)# be the point that divides #bar(AB)# in the ratio #k :1#, where #k>0#. Show that #x= (x_a+kx_b)/ (1+k)# and #y= (y_a+ky_b)/( 1+k)#?
- What is the orthocenter of a triangle with corners at #(2 ,3 )#, #(6 ,1 )#, and (6 ,3 )#?
- What is the orthocenter of a triangle with corners at #(2 ,8 )#, #(3 ,4 )#, and (6 ,3 )#?
- Maya drives from New York City to Boston at a rate of 40 MPH and drives at a rate of 60 MPH on the return trip. What was his average speed for the entire trip? Use the Harmonic mean to compute? Construct the HM geometrically?
- How do you find the perpendicular bisectors of a triangle?

- 98% accuracy study help
- Covers math, physics, chemistry, biology, and more
- Step-by-step, in-depth guides
- Readily available 24/7