On a piece of graph paper, plot the following points: A (0, 0), B (5, 0), and C (2, 4).
These coordinates will be the vertices of a triangle. Using the Midpoint Formula, what are the midpoints of the triangle's side, segments AB, BC, and CA?

Question

On a piece of graph paper, plot the following points: A (0, 0), B (5, 0), and C (2, 4). 
These coordinates will be the vertices of a triangle. Using the Midpoint Formula, what are the midpoints of the triangle's side, segments AB, BC, and CA?

Avery Allen · Accepted Answer

#color(blue)((2.5,0), (3.5,2), (1,2)#

We can find all the midpoints before we plot anything. We have sides:

#AB, BC, CA#

The co-ordinates of the midpoint of a line segment is given by:

#((x_1+x_2)/2,(y_1+y_2)/2)#

For #AB# we have:

#((0+5)/2,(0+0)/2)=>(5/2,0)=>color(blue)((2.5,0)#

For #BC# we have:

#((5+2)/2,(0+4)/2)=>(7/2,2)=>color(blue)((3.5,2)#

For #CA# we have:

#((2+0)/2,(4+0)/2)=>color(blue)((1,2)#

We now plot all the points and construct the triangle:

James Atkins · Answer

undefined The midpoints of the sides of the triangle with vertices A (0, 0), B (5, 0), and C (2, 4) are:

1. Midpoint of AB:
   $$ \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right) $$
   Substituting the coordinates of A and B:
   $$ \left( \frac{0 + 5}{2}, \frac{0 + 0}{2} \right) = \left( \frac{5}{2}, 0 \right) $$

2. Midpoint of BC:
   Substituting the coordinates of B and C:
   $$ \left( \frac{5 + 2}{2}, \frac{0 + 4}{2} \right) = \left( \frac{7}{2}, 2 \right) $$

3. Midpoint of CA:
   Substituting the coordinates of C and A:
   $$ \left( \frac{2 + 0}{2}, \frac{4 + 0}{2} \right) = \left( 1, 2 \right) $$

So, the midpoints of the sides AB, BC, and CA are: 
Midpoint of AB: (2.5, 0)
Midpoint of BC: (3.5, 2)
Midpoint of CA: (1, 2).

On a piece of graph paper, plot the following points: A (0, 0), B (5, 0), and C (2, 4). These coordinates will be the vertices of a triangle. Using the Midpoint Formula, what are the midpoints of the triangle's side, segments AB, BC, and CA?