Question

The midpoint of diagonal BD of rhombus is (3, 4) if the coordinate of B(1, 5) the coordinate of D is​

Answer 1

The coordinate of D is ( 5, 3 ).

Given: The midpoint of diagonal BD of a rhombus is ( 3, 4 ) and the coordinate of B is ( 1, 5 ).

To Find: The coordinate of D.

Solution:

The mid-point of two coordinates ( x1, y1 ) and ( x2, y2 ) can be found by using the formula,

          Mid-point (M) ≡ (( x1 + x2 ) / 2 ) , ( y1 + y2 ) / 2 ))                  ...(1)

Coming to the numerical, we are given;

The mid-point ≡ ( 3, 4 )

The coordinate of B is = ( 1, 5 )

Let the coordinate of D be ( x, y )

Putting respective values in (1), we get;

        Mid-point (M) ≡ (( x1 + x2 ) / 2 ) , ( y1 + y2 ) / 2 ))        

    ⇒ ( 3, 4 ) ≡ (( 1 + x ) / 2 , ( 5 + y ) / 2 )

∴ ( 1 + x ) / 2  =  3   and   ( 5 + y ) / 2 = 4

First solving ( 1 + x ) / 2  =  3, we get;

    ⇒ ( 1 + x ) / 2  =  3

    ⇒ x + 1 = 6

    ⇒  x = 5

Now, solving ( 5 + y ) / 2 = 4, we get;

    ⇒ ( 5 + y ) / 2 = 4

    ⇒  5 + y = 8

    ⇒   y = 3

The point is ( 5, 3 ).

Hence, the coordinate of D is ( 5, 3 ).

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