A line segment is bisected by a line with the equation #  6 y + 2 x = 4 #. If one end of the line segment is at #( 4 , 8 )#, where is the other end?
The other point is
By signing up, you agree to our Terms of Service and Privacy Policy
To find the other end of the line segment bisected by the line ( 6y + 2x = 4 ) with one end at (4, 8):

Find the slope of the given line. Rearrange the equation to slopeintercept form: ( y = \frac{1}{3}x  \frac{2}{3} ). The slope is ( \frac{1}{3} ).

Since the line bisects the line segment, the slope of the perpendicular bisector is the negative reciprocal of ( \frac{1}{3} ), which is ( 3 ).

Use the midpoint formula to find the midpoint of the line segment, which is also the point on the bisecting line: [ \left(\frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2}\right) ]

Given one endpoint (4, 8), use the midpoint formula and the slope to find the other endpoint.
[ x = \frac{4 + x_2}{2} ] [ y = \frac{8 + y_2}{2} ]

Substitute the equation of the bisecting line ( 6y + 2x = 4 ) into the equations above and solve for ( x ) and ( y ).

Once ( x ) and ( y ) are found, the coordinates ( (x, y) ) represent the other end of the line segment.
By signing up, you agree to our Terms of Service and Privacy Policy
When evaluating a onesided 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 onesided 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 onesided 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 onesided 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.
 What is the orthocenter of a triangle with corners at #(6 ,3 )#, #(2 ,4 )#, and (7 ,9 )#?
 A line segment is bisected by line with the equation # 6 y  2 x = 1 #. If one end of the line segment is at #(2 ,5 )#, where is the other end?
 Let #l# be a line described by equation ax+by+c=0 and let #P(x,y)# be a point not on #l#. Express the distance, #d# between #l and P# in terms of the coefficients #a, b and c# of the equation of line?
 What is the orthocenter of a triangle with corners at #(5 ,9 )#, #(4 ,3 )#, and (1 ,2 )#?
 A triangle has corners A, B, and C located at #(3 ,1 )#, #(6 ,7 )#, and #(9 ,8 )#, respectively. What are the endpoints and length of the altitude going through corner C?
 98% accuracy study help
 Covers math, physics, chemistry, biology, and more
 Stepbystep, indepth guides
 Readily available 24/7