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

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

Step-by-step 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 = $(\dfrac{x_1+x_2}{2},\dfrac{y_1+y_2}{2})$

$=(\dfrac{-2+4}{2},\dfrac{2+(-2)}{2})=(1,0)$

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

Mid point of IK = $(\dfrac{x_1+x_2}{2},\dfrac{y_1+y_2}{2})$

$=(\dfrac{4+(-2)}{2},\dfrac{3+(-3)}{2})=(1,0)$

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.