MATH SOLVE

2 months ago

Q:
# Prove: The segments joining the midpoints of the opposite sides of a quadrilateral bisect each other.Midpoints of both segments are the same point; therefore, segments bisect each other.(fill in the blanks of the equation in the second picture with the correct number/letter/sign based off the first picture.)

Accepted Solution

A:

Answer:[tex]R=(\dfrac{b}{2},0)[/tex][tex]S=(\dfrac{b+c}{2},\dfrac{d}{2})[/tex][tex]T=(\dfrac{c+e}{2},\dfrac{d+f}{2})[/tex][tex]U=(\dfrac{e}{2},\dfrac{f}{2})[/tex][tex]M=(\dfrac{b+c+e}{4},\dfrac{d+f}{4})[/tex][tex]M=(\dfrac{c+b+e}{4},\dfrac{d+f}{4})[/tex]Step-by-step explanation:We are given coordinates as:[tex]A(0,0)\ ,\ B=(b,0)\ ,\ C=(c,d)\ ,\ D=(e,f)\\\\R=(\dfrac{b}{2},0)\ ,\ S=(\dfrac{b+c}{2},\dfrac{d}{2})\ ,\ U=(\dfrac{e}{2},\dfrac{f}{2})\ ,\ T=(\dfrac{c+e}{2},\dfrac{d+f}{2})[/tex]Now, it is given that M is the mid-point of the line segment RT and of US.Hence, the coordinates of M is given as:By taking the mid-point of side RT.[tex]M=(\dfrac{\dfrac{b}{2}+\dfrac{c+e}{2}}{2},\dfrac{0+\dfrac{d+f}{2}}{2}})\\\\\\i.e.\\\\\\M=(\dfrac{b+c+e}{4},\dfrac{d+f}{4})[/tex]By taking the mid-point of side US.[tex]M=(\dfrac{\dfrac{e}{2}+\dfrac{b+c}{2}}{2},\dfrac{\dfrac{f}{2}+\dfrac{d}{2}}{2})\\\\\\i.e.\\\\\\M=(\dfrac{b+c+e}{4},\dfrac{d+f}{4})[/tex]