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?

Jun 10, 2018

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

Explanation:

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

$A B , B C , C A$

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

$\left(\frac{{x}_{1} + {x}_{2}}{2} , \frac{{y}_{1} + {y}_{2}}{2}\right)$

For $A B$ we have:

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

For $B C$ we have:

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

For $C A$ we have:

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

We now plot all the points and construct the triangle: