let PQRS be a quadrilateral if M and N are the midpoints of the sides PQ and RS - Maths -

Question

let PQRS be a quadrilateral if M and N are the midpoints of the
sides PQ and RS respectively then prove that PS- +
QR- =2MN-
here - means bar

Brijendra Pal · Accepted Answer

Dear Student,
<img alt="" src=
"https://s3mn%20mnimgs%20com/img/shared/ck-files/ck_578e6f571ce21%20png"
style="width: 373px; height: 337px;">
Let P = x,y Q =a,bR= m,nS =u,vSo PS+ QR = m-ai+n-bj+ u-xi+v-yj=m-a+u-xi+n+v-y-bj
1Now M = x+a2,y+b2 and N = m+u2,n+v2 MN =m+u2-x+a2 i+n+v2-y+b2j=12m+u-a-xi+12n+v-y-bjSo 2MN = m-a+u-xi+n+v-y-bj= PS+ QRUsing equation 1
 Regards

let PQRS be a quadrilateral . if M and N are the midpoints of the sides PQ and RS respectively then prove that PS- + QR- =2MN- here - means bar

let PQRS be a quadrilateral . if M and N are the midpoints of the sides PQ and RS respectively then prove that PS^- + QR^-=2MN-
here ^- means bar