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Three consecutive vertices of a parallelogram ABCD are A(1, 2), B(1, 0) and C(4, 0). The co – ordinates of the fourth vertex D are
  • a)
    (– 4, – 2)
  • b)
    (4, – 2)
  • c)
    (– 4, 2)
  • d)
    (4, 2)
Correct answer is option 'D'. Can you explain this answer?
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Verified Answer
Three consecutive vertices of a parallelogram ABCD are A(1, 2), B(1, 0...
Let coordinates of D be (x, y).
Since diagonals of a parallelogram bisect each other.
Therefore, coordinates of O will be 

Therefore, the required coordinates are (4, 2).
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Most Upvoted Answer
Three consecutive vertices of a parallelogram ABCD are A(1, 2), B(1, 0...
Ordinate of the fourth vertex D can be found as follows:

Since AB is parallel to CD, the slope of AB must be equal to the slope of CD. The slope of AB is:

mAB = (0 - 2)/(1 - 1) = undefined

This is because the line AB is a vertical line. Therefore, CD must also be a vertical line passing through point C(4,0).

So, the x-coordinate of point D must be 4. To find the y-coordinate, we use the fact that AD is parallel to BC, so the slope of AD must be equal to the slope of BC. The slope of BC is:

mBC = (0 - 2)/(4 - 1) = -2/3

Therefore, the slope of AD is also -2/3. We can use this slope and the point A(1,2) to find the equation of line AD:

y - 2 = (-2/3)(x - 1)

y - 2 = (-2/3)x + 2/3

y = (-2/3)x + 8/3

Now, we can substitute x = 4 into this equation to find the y-coordinate of point D:

y = (-2/3)(4) + 8/3

y = -8/3 + 8/3

y = 0

Therefore, the fourth vertex of the parallelogram is D(4,0).
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Three consecutive vertices of a parallelogram ABCD are A(1, 2), B(1, 0) and C(4, 0). The co – ordinates of the fourth vertex D area)(– 4, – 2)b)(4, – 2)c)(– 4, 2)d)(4, 2)Correct answer is option 'D'. Can you explain this answer?
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