ABCD is a parallelogram. If coordinates of A,B,C are (2,3), (1,4) and (0, -2). Coordinates of D =a)(-1,3)b)(1,-3)c)(1,3)d)(-1,-3)Correct answer is option 'B'. Can you explain this answer?

Question

ABCD is a parallelogram. If coordinates of A,B,C are (2,3), (1,4) and (0, -2). Coordinates of D =&#8203;a)(-1,3)b)(1,-3)c)(1,3)d)(-1,-3)Correct answer is option 'B'. Can you explain this answer?

Answer

Here's a generic way to solve problems like this.

Answer

I f u have have given three coordinate of vertices of
llgm then to find fourth coordinate bhave to add adjacent coordinate and then subtract opposite coordinate.
like D= A+C - B=(2+0 - 1, 3+(-2) -4)=(1,-3)

Answer

To find the coordinates of point D in the parallelogram ABCD, we can use the properties of a parallelogram. One such property is that opposite sides of a parallelogram are equal in length and parallel.

Step 1: Find the vector representing AB
The vector AB is given by subtracting the coordinates of point A from point B:
AB = (1-2, 4-3) = (-1, 1)

Step 2: Find the coordinates of point D using the vector AB
To find the coordinates of point D, we add the vector AB to the coordinates of point C:
D = (0, -2) + (-1, 1) = (-1, -1)

Therefore, the coordinates of point D in the parallelogram ABCD are (-1, -1).

Let's check if the parallelogram property holds true by calculating the lengths of the opposite sides.

Step 3: Calculate the lengths of opposite sides
Using the distance formula, we can calculate the lengths of the sides of the parallelogram:
AB = √((-1-2)^2 + (1-3)^2) = √(9 + 4) = √13
BC = √((0-1)^2 + (-2-4)^2) = √(1 + 36) = √37
CD = √((0-(-1))^2 + (-2-(-1))^2) = √(1 + 1) = √2
DA = √((2-(-1))^2 + (3-(-1))^2) = √(9 + 16) = √25 = 5

We can see that AB and CD have the same length (√13), and BC and DA also have the same length (5). This confirms that ABCD is a parallelogram.

Conclusion:
The coordinates of point D in the parallelogram ABCD are (-1, -1). Therefore, the correct answer is option 'B' (1, -3).

Answer

(1,-3) if we have 3 co-ordinates of parallelogram then we can find it easily with the help of slopes bcoz slope of parallel lines are equal

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