Question

$A(-2,2),B(8,2)$ and $C(4,-4)$ are the vertices of a parallelogram $ABCD$. By plotting the given points on a graph paper; find the co-ordinates of the fourth vertex $D$.
Also, from the same graph, state the co-ordinates of the mid-points of the sides $AB$ and $CD$.

• A. $D=(-6,4);$ Mid-point of $AB=(5,2)$ and mid-point of $CD=(-1,4)$
• B. $D=(-6,-4);$ Mid-point of $AB=(3,2)$ and mid-point of $CD=(-1,-4)$
• C. $D=(6,4);$ Mid-point of $AB=(3,2)$ and mid-point of $CD=(5,4)$
• D. $D=(-6,-4);$ Mid-point of $AB=(5,2)$ and mid-point of $CD=(-1,-4)$

Answer 1

Answer: (B)

$D=(-6,-4);$ Mid-point of $AB=(3,2)$ and mid-point of $CD=(-1,-4)$

Plot the points A, B, and C on the graph paper. Join the points to complete the parallelogram ABCD. As the distance between points A and B is 10 units, distance between the corners of the opposite side C and D will also be 10 units.
Hence, the fourth point D $=(-6,-4)$
Mid point of AB will lie at 5 units distance from A and B both which is $=(3,2)$
Mid point of CD will lie at 5 units distance from C and D both which is $=(-1,-4)$