Points A(-2, 4). B(1.3), C(4, -1) and D form a parallelogram. What are the coordinates of D?
A. (5.5)
B. (0,0)
C. (1.-2)
D. (1,0)
E. (34)

Option D. (1,0)

Step-by-step explanation:

See the attached figure.

The properties of the parallelogram: each two opposite sides are parallel.

As shown at the graph:

We have two sides of the parallelogram which are AB and BC (blue color)

We need to select which point from the red points is suitable to form the parallelogram.

It is clear that the points (3,4) and (5,5) are absolutely wrong points.

For the points (1,-2) and (0,0) also wrong choices, It will not make CD//AB

We will check the point (1,0)

So, if D = (1,0)

The slope of the line AB = (3-4)/(1- -2) = -1/3

And the slope of CD = (0- -1)/(1-4)= -1/3

So, the slope of AB = slope of CD ⇒ (1)

The slope of BC = (-1-3)/(4-1) = -4/3

And the slope of AD = (0-4)/(1- -2) = -4/3

So, slope of BC = slope of AD ⇒(2)

From (1) and (2):

So, to form a parallelogram, the point D is (1,0)

The answer is option D. (1,0)

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