the points (0,10),(5,5),(1,1) and (-4,6) are vertices of a rectangle. Determine the coordinates of the midpoints for each side and determine if the midpoints are the vertices or a rectangle.

Question

the points (0,10),(5,5),(1,1) and (-4,6) are vertices of a rectangle.  Determine the coordinates of the midpoints for each side and determine if the midpoints are the vertices or a rectangle.

anonymous · Answer

Simple the formula for mid point is M ={ (x1+x2)/2, (y1+y2)/2} 
Now using this formula take out the mid points of all the sides of rectangle whose vertices are the mid points
Now use distance formula
$$D=\sqrt{(x2-x1)^{2}+(y2-y1)^{2}}$$
now if the the opposite sides of the second figure are equal then the figure is rectangle