Question

If a(1,2) b(4,y) c(x,6) d(3,5) are thr vertices of a parallelogram taken in order find x and y

Answer 1

If (1, 2), (4, y), (x, 6) and (3, 5) are the vertices of a parallelogram taken in order, find x and y. Let the points be A(1, 2) , B(4, y) , C(x, 6) , D(3, 5) We know that diagonals of parallelogram bisect each other So, O is the mid pint of AC & BD Finding mid point of AC We have to find co ordinates of O x coordinate of O = ( 1 + 2)/2 y coordinate of O = ( 1 + 2)/2 Where x1 = 1 , y1 = 2 x2 = x , y2 = 6 Putting values for x coordinate x coordinate of O = (1 + )/2 Putting values for y coordinate y coordinate of O = (2 + 6)/2 = 8/2 = 4 Hence, coordinates of O = ((1 + )/2 , 4) Finding mid point of BD, We find coordinates of O x coordinate of O = ( 1 + 2)/2 y coordinate of O = ( 1 + 2)/2 x1 = 4 , y1 = y x2 = 3 , y2 = 5 Putting values for x coordinate x coordinate of O = (4 + 3)/2 x coordinate of O = 7/2 Putting values for y coordinate y coordinate of O = ( + 5)/2 Hence, coordinates of O = (7/2 , ( + 5)/2) From (1) & (2) ((1 + )/2 , 4) = (7/2 , ( + 5)/2) Comparing x & y coordinates Hence , x = 6 , y = 3

Answer 2

Answer:

Step-by-step explanation: