Question

The diagram shows a rhombus ABCD. The points B and D have co-ordinates (2,
10) and (6,2) respectively, and A lies on X-axis. The mid-point of BD is M.

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Answer 1

Given : a rhombus ABCD. The points B and D have co-ordinates (2,

10) and (6,2) respectively,

A lies on X-axis. The mid-point of BD is M.

To Find :  Coordinates of A, C & M

Solution:

Diagonals of rhombus bisect each other perpendicularly

M is mid point of  B (2 , 10) and D( 6 , 2)

M = (2 + 6)/2 , ( 10 + 2)/2

= 4 , 6

M = ( 4 ,6 )

Slope of BD  =  (2 - 10)/(6 - 2)  = -8/4  = - 2

Slope of C = - 1/(-2)  = 1/2

AC  equation  =   y - 6  = (1/2)(x - 4)

=> 2y - 12 = x - 4

=> 2y  = x + 8

A lies on X-axis.

=> y = 0

=> 0 = x + 8

=> x = - 8

A = ( -8 , 0)

M is mid point of AC

=>  C  =  (x , y)

(-8 + x)/2  = 4   , (0 + y)/2  = 6

=> x = 16 and y = 12

C = ( 16 , 12)

M = ( 4 ,6 )

A = ( -8 , 0)

C = ( 16 , 12)

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