Question

If A (-2, -1), B (a, 0), C (4, b) and D (1,2) are the vertices of parallelogram, find the
values of a and b.
OR
If the mid-point of the line joining (3, 4) and (k, 7) is (x, y) and 2x+2y+1=0 find the
value of k.

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Answer 1

Step-by-step explanation:

If it is vertices of parallelogram then AB2=CD2 and AD2=BC2

AB2=CD2

(-2-a)2+(-1-0)2=(4-1)2+(b-2)2

4+4a-a2+1=9+b2-4b+4

4a-a2+1=9+b2-4b

4a-a2=8+b2-4b

a(4-a)=8+b(b-4)

4+4=8+a+b

8=8+a+b

0=a+b