posted by .

Find the bisectors of the interior angles of the triangle whose sides are the line 7x+y-7=0, x+y+1=0 and x+7y-4=0.

Please I really need help. I do not know how to do this problem

  • geometry -

    It really helps to draw a diagram, so you know which three angles you're dealing with. Label the three lines L1,L2,L3 in order.

    First, get the slope of each line:

    L1: -7
    L2: -1
    L3: -1/7

    Now convert those slopes to angles, measured counter-clockwise from the x- axis:

    L1: θ = 98.13°
    L2: θ = 135.00°
    L3: θ = 171.87°

    Now, the angle bisector is the average of the two angles made by the lines:

    B1: (L1+L2)/2 = 116.57° tan = -2
    B2: (L2+L3)/2 = 153.43° tan = -1/2
    B3: (L1+L3)/2 = -135.00° tan = 1

    Now you need the intersections of the lines:

    P1(L1=L2): (4/3, -7/3)
    P2(L2=L3): (-11/6, 5/6)
    P3(L1=L3): (15/16, 7/16)

    Now we have a point-slope for each angle bisector:

    B1: (y+7/3) = -2(x-4/3)
    B2: (y-5/6) = -1/2 (x+11/6)
    B3: (y-7/16) = 1(x-15/16)
    B1: 6x+3y-1 = 0
    B2: 6x+12y+1 = 0
    B3: 2x-2y-1 = 0

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. Math

    line BC is one side of a regular n-gon. The sides next to line BC are extended to meet at W. Find the measure of angle W in terms of n That's a triangle. Use the facts about the relationships between the angles. If the ngon is regular, …
  2. Geometry

    The measure of an exterior angle of a triangle is 120. the interior angles that are not adjacent to this exterior angle are congruent. find the measures of the interior angles of the triangle

    Where is the circumcenter of any given triangle?
  4. Geometry

    1) In the diagram above, line a is parallel to line b. Which theorem or postulate allows you to conclude that angle 6 is equal to 8?
  5. geometry

    In a triangle ABC , the internal bisectors of angles B and C meet at P and the external bisectors of the angles B and C meet at Q. prove that: angle BPC + angle BQC = 2 rt. angles.
  6. Geometry

    Please answer at least one . PLEASE 1. Triangle XYZ has a right angle at Y. V,W are on XZ such that XV=XY. WZ=YZ, find ANGLE VYW . 2. STUVWXYZ is a regular octagon. Find SW/ TZ. 3. The interior angles of a convex polygon form an arithmetic …
  7. Math! Please check!

    When constructing the circumcenter and circumscribed circle of a triangle, you need to find the intersection of all three of which type of line?
  8. Analytic Geometry

    Find the bisectors of the interior angles of the triangle whose sides are the line 7x+y-7=0, x+y+1=0 and x+7y-4=0.
  9. geometry

    Prove that the angle bisectors of the base of the isosceles angles of the isosceles triangle are congruent using statement and reason proof i dont really now how to prove this problem but i now what a transversal is and the angles …
  10. Geometry

    The parallelogram has the angle measuers shown. Can you conclude that it is a rhombus, a rectangle, or a square?

More Similar Questions