Question

Two segments of Parallelogram ABCD are shown below.    Which coordinate pair BEST represents the location of Point D, the fourth vertex of Parallelogram ABCD? A. (6, 1)  B. (7, 0) C. (8,2) D. (7,1)

Answer 1

Given coordinates of A(2,-1), B(1,3), C(6,5)

Let the coordinates of D(x,y)

Let join AC and BD:

SO by mid point rule:

Coordinates of midpoint by AC are:

`((2+6)/(2),\text{ }(-1+5)/(2))\rightarrow(4,2)`

And the midpoint of BD are same as AC:

`\begin{gathered} (1+x)/(2)=4 \\ 1+x=8 \\ x=7 \end{gathered}`
`\begin{gathered} (3+y)/(2)=2 \\ 3+y=4 \\ y=4-3 \\ y=1 \end{gathered}`

hence the coordinates of D are (7,1)

Option D is correct.