Equations for Symmetric Lines in Triangle ABC

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In summary, the equations for the symmetric lines of two inner angles of triangle ABC are x+4=0 and 4x+7y+5=0, and the equation for one of the sides of the triangle is 3x+4y=0. To find the equations of the lines for the other two sides of the triangle, we can use the formula d=\frac{|Ax + By + C|}{|\sqrt{A^2+B^2}|} and the given point (0,0).
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Homework Statement



The equations of the symmetric lines of two inner angles of triangle ABC are given:

x+4=0 and 4x+7y+5=0, and the equation of the line of one of the sides of the triangle is

given 3x+4y=0 (which goes through the points of the side where the symmetric lines are

going). Find the equations of the lines which are going among the other two sides of the

triangle.

Homework Equations




[tex]d=\frac{|Ax + By + C|}{|\sqrt{A^2+B^2}|}[/tex]


The Attempt at a Solution



I found one of the dots A(-4,3). Also I find that the lines are going through the point (0,0)
 
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  • #2
By "symmetric line" of an angle, do you mean the angle's bisector?
 
  • #3
HallsofIvy said:
By "symmetric line" of an angle, do you mean the angle's bisector?

yes, sorry for mistranslation.
 
  • #4
anybody know?
 

1. How do you find the equations for symmetric lines in triangle ABC?

To find the equations for symmetric lines in triangle ABC, you first need to identify the line of symmetry. This can be done by drawing a perpendicular bisector of one of the sides of the triangle. Once you have the line of symmetry, you can use the slope-intercept form of a line to write the equation.

2. What is the formula for finding the slope of a line of symmetry in a triangle?

The formula for finding the slope of a line of symmetry in a triangle is m = -1/((y2-y1)/(x2-x1)), where (x1,y1) and (x2,y2) are two points on the line. This formula is derived from the fact that the line of symmetry is perpendicular to the side of the triangle.

3. Can the equations for symmetric lines in triangle ABC be used to find the coordinates of the vertices?

No, the equations for symmetric lines in triangle ABC can only be used to find the equations of the lines. To find the coordinates of the vertices, you will need additional information such as the coordinates of one vertex and the lengths of the sides of the triangle.

4. Are the equations for symmetric lines in triangle ABC always linear?

Yes, the equations for symmetric lines in triangle ABC are always linear. This is because the line of symmetry is always a straight line, and the equations for symmetric lines are derived from the slope-intercept form of a line.

5. Is it possible for a triangle to have more than one line of symmetry?

Yes, it is possible for a triangle to have more than one line of symmetry. An equilateral triangle, for example, has three lines of symmetry, while an isosceles triangle has only one line of symmetry. The number of lines of symmetry a triangle has depends on its shape and angles.

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