Perpendicular Bisector & Altitude of Triangle: A(4;2) B(11;6) C(-3;-1)

The point of intersection can be found by solving the system of equations formed by the two lines. This can be done by using substitution or elimination methods.
  • #1
adod
1
0
The vertices of a triangle are A(4;2) ; B(11;6) ; C(-3;-1)
What is the equation of the perpendicular bisector of side a?
(i think -7x+14y=7)
What is the equation of the altitude of side c?
(i think -4x+7y=5)
What is the intersection of the previous lines?
i have no idea about this,please help,and also write down how you solved it
 
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  • #2
adod said:
The vertices of a triangle are A(4;2) ; B(11;6) ; C(-3;-1)
What is the equation of the perpendicular bisector of side a?
(i think -7x+14y=7)
What is the equation of the altitude of side c?
(i think -4x+7y=5)
What is the intersection of the previous lines?
i have no idea about this,please help,and also write down how you solved it

Welcome to PH (=
what is side a? AB? AC ? BC?
 
  • #3
Side a is usually the side across from angle A.

How does one normally find the point of intersection of two lines?
 

FAQ: Perpendicular Bisector & Altitude of Triangle: A(4;2) B(11;6) C(-3;-1)

What is a perpendicular bisector?

A perpendicular bisector is a line that divides a line segment into two equal parts at a 90 degree angle. It passes through the midpoint of the line segment.

What is an altitude of a triangle?

An altitude of a triangle is a line segment drawn from a vertex of the triangle to the opposite side, forming a right angle. It represents the height of the triangle.

How do you find the equation of the perpendicular bisector of a line?

The equation of a perpendicular bisector can be found by first finding the slope of the line using the formula (y2 - y1) / (x2 - x1). Then, to find the slope of the perpendicular bisector, take the negative reciprocal of the original slope (-1/m). Finally, use the midpoint formula ((x1 + x2)/2, (y1 + y2)/2) to find the coordinates of the midpoint, and plug in the new slope and midpoint into the slope-intercept form of a line (y = mx + b) to find the equation.

How do you find the equation of the altitude of a triangle?

The equation of the altitude of a triangle can be found by first finding the slope of the side opposite the vertex where the altitude is drawn. Then, use the point-slope form of a line (y - y1 = m(x - x1)) with the slope and the coordinates of the vertex to find the equation.

How do you find the point of intersection between the perpendicular bisector and altitude of a triangle?

The point of intersection between the perpendicular bisector and altitude can be found by setting the equations of the two lines equal to each other and solving for the coordinates of the point. This point will be the circumcenter of the triangle, which is the center of the circle that can be circumscribed around the triangle.

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