Question

State whether the following statements are true or false.
Enter $1$ for true and $0$ for false

Points A (4, 3), B (6, 4), C (5, 6) and D (3, 5) are the vertices of a parallelogram.

Answer 1

$LetthepointsA=(x_1,y_1)=(4,3),B=(x_2,y_2)=(6,4),C=(x_3,y_3)=(5,6)\&D={(x}_4,y_4)=(3,5)formaparallelogram.Then,bythepropertyofparallelogramsthatthediagonalsofaparallelogrambisecteachother,themidpointsofAC\&BDshouldbethesamepoint.ThemidpointofAC=(\frac{x_1+x_3}{2},\frac{y_1+y_3}{2})=(\frac{4+5}{2},\frac{3+6}{2})=(4.5,4.5).ThemidpointofBD=(\frac{x_2+x_4}{2},\frac{y_2+y_4}{2})=(\frac{6+3}{2},\frac{4+5}{2})=(4.5,4.5).SincethemidpointsofAC\&BDarethesame,\therefore ABCDisaparallelogram.Sothestatementistrue.Ans-TRUE.$