Question

On a coordinate plane, parallelogram H I J K is shown. Point H is at (negative 2, 2), point I is at (4, 3), point J is at (4, negative 2), and point K is at (negative 2, negative 3). HIJK is a parallelogram because the midpoint of both diagonals is __________, which means the diagonals bisect each other

Answer 1

(1,0)

Explanation:

Answer 2

Answer: HIJK is a parallelogram because the midpoint of both diagonals is (1,0) , which means the diagonals bisect each other.

Explanation:

Given: The coordinates of parallelogram H I J K as

H is at (- 2, 2), point I is at (4, 3), point J is at (4, - 2), and point K is at (- 2, - 3).

Diagonals : HJ and IK [join opposite vertices]

Mid point of HJ =
`((x_1+x_2)/(2),(y_1+y_2)/(2))`

`=((-2+4)/(2),(2+(-2))/(2))=(1,0)`

i.e. Mid point of HJ = (1,0)

Mid point of IK =
`((x_1+x_2)/(2),(y_1+y_2)/(2))`

`=((4+(-2))/(2),(3+(-3))/(2))=(1,0)`

i.e. Mid point of IK = (1,0) =Mid point of HJ

When mid points of both diagonals are equal then that means the diagonals bisect each other.

Thus, HIJK is a parallelogram because the midpoint of both diagonals is (1,0) , which means the diagonals bisect each other.