# Vertices of triangle, multi-problems

• rocomath

#### rocomath

Vertices of triangle ABC are A(2a,0), B(2b,0), C(0,2).

a) Find the equations of the sides (check, did that)

AB: y=0
AC: x+ay=2a
BC: x+by=2b

I'm having trouble with b)

Show that the equations of the medians are: x+(2a-b)y=2a, x+(2b-a)y=2b, 2x+(a+b)y=2(a+b)

Ok, they're not referring to the midpoints of AB, AC, and BC? I think that's where my mistake is. The median is point of intersection where a line intersects each line at each line's midpoint and meets at a common center point inside the triangle?

Part of your objective is to find the midpoint of each side because that is an essential component of Median of a Triangle. The point in the interior of the triangle at which the medians intersect is of no concern in the answer.

Vertices of triangle ABC are A(2a,0), B(2b,0), C(0,2).

a) Find the equations of the sides (check, did that)

AB: y=0
AC: x+ay=2a
BC: x+by=2b

I'm having trouble with b)

Show that the equations of the medians are: x+(2a-b)y=2a, x+(2b-a)y=2b, 2x+(a+b)y=2(a+b)

Ok, they're not referring to the midpoints of AB, AC, and BC? I think that's where my mistake is. The median is point of intersection where a line intersects each line at each line's midpoint and meets at a common center point inside the triangle?

No. A "median" of a triangle is the line segment from one vertex to the midpoint of the opposite side. For example, the midpoint of AB is (a+b, 0) and C is (0,2). What is the equation of that line?

... isn't quite right. Hint: What is the y-int of lines connecting A and C ? A and B?

Sorry, I meant B and C?

... isn't quite right. Hint: What is the y-int of lines connecting A and C ? A and B?

Sorry, I meant B and C?
?

The equations given were AC: x+ay=2a and BC: x+by=2b with A= (2a,0), B= (2b, 0), and C= (0, 2). When x= 2a, the first equation gives 2a+ ay= 2a or y= 0 and when x= 0 it gives ay= 2a or y= 2. When x= 2b, the second equation gives 2b+ by= 2b or y= 0 and when x= 0 it gives by= 2b so y= 2. Exactly what is wanted.

D'oh

Yup, yup and yup. Sheesh, the careless algebra mistakes I can make are embarrassing. thanks H.O.V.