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

HIJK is a parallelogram because the midpoint of both diagonals is

(1 , 0), which means the diagonals bisect each other

Step-by-step explanation:

If (x , y) is the mid-point of a segment whose end points are $(x_{1},y_{1})$  and  $(x_{2},y_{2})$  then,

• $x=\frac{x_{1}+x_{2}}{2}$

• $y=\frac{y_{1}+y_{2}}{2}$

In a parallelogram, its diagonals intersect each other at their mid-points

that means its diagonals bisect each other

∵ HIJK is a quadrilateral

∵ HJ and IK are its diagonals

∵ H = (-2 , 2)

∵ J = (4 , -2)

- Find the mid point of HJ  

∵ $M_{HJ}=(\frac{-2+4}{2},\frac{2+-2}{2})$

∴ $M_{HJ}=(\frac{2}{2},\frac{0}{2})$

∴ $M_{HJ}=(1,0)$

∴ The mid-point of HJ is (1 , 0)

∵ I = (4 , 3)

∵ K = (-2 , -3)

- Find the mid point of IK  

∵ $M_{IK}=(\frac{4+-2}{2},\frac{3+-3}{2})$

∴ $M_{IK}=(\frac{2}{2},\frac{0}{2})$

∴ $M_{IK}=(1,0)$

∴ The mid-point of IK is (1 , 0)

∵ The mid-points of HJ and IK are equal

∴ HJ and IK bisects each other

∴ HIJK is a parallelogram because its diagonals bisect each other

HIJK is a parallelogram because the midpoint of both diagonals is

(1 , 0), which means the diagonals bisect each other

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Answer 2

Answer:

(1,0)

Step-by-step explanation: