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Three of the vertices of a parallelogram are A(2, 4), B(6,2) and C (8, 6).(a) Plot the point A, B and C in the coordinate plane(b) Find the mid-point of diagonal AC(c) Find the fourth vertex D(d) Find the length of diagonal AC(e) Find the perimeter of ABCD.

User Roberts
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1 Answer

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Given:

Three of the vertices of a parallelogram are given as


\begin{gathered} A\left(2,4\right)_ \\ B\left(6,2\right) \\ C(8,6) \end{gathered}

Required:

(a) Plot the point A, B and C in the coordinate plane

(b) Find the mid-point of diagonal AC

(c) Find the fourth vertex D

(d) Find the length of diagonal AC

(e) Find the perimeter of ABCD.

Step-by-step explanation:

Take D coordinate as (x,y)

now midpoint of AC and BD is same so


\begin{gathered} ((2+8)/(2),(4+6)/(2))=((x+6)/(2),(2+y)/(2)) \\ \\ (5,5)=((x+6)/(2),(2+y)/(2)) \\ \\ x=4,y=8 \end{gathered}

midpoint of AC


((2+8)/(2),(4+6)/(2))=(5,5)

length of diagonal AC


AC=√(36+4)=2√(10)

perimeter of ABCD


AB=√(16+4)=√(20)
BC=√(4+16)=√(20)

perimeter is


2(AB+BC)=4√(20)

Final answer:

(b) Find the mid-point of diagonal AC


\begin{equation*} (5,5) \end{equation*}

(c) Find the fourth vertex D


(4,8)

(d) Find the length of diagonal AC


2√(10)

(e) Find the perimeter of ABCD.


\begin{equation*} 4√(20) \end{equation*}

Three of the vertices of a parallelogram are A(2, 4), B(6,2) and C (8, 6).(a) Plot-example-1
User Zubair Hassan
by
7.8k points

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