Question

HIJK is a parallelogram because the midpoint of both diagonals is ____ which means the diagonals bisect each other.

A. (1,-1)
B. (1,1)
C. (1,0)
D. (0,1)

HELP QUICKLY PLEASE!!!!!

Answer 1

ANSWER

The midpoint of both diagonals is

$(1,0)$
EXPLANATION

We can use either diagonals to determine the midpoint.

We use the midpoint formula

$( \frac{x_1 + x_2}{2} , \frac{y_1 + y_2}{2} )$

Let us use the first diagonals H(-2,2) and J(4,-2)

$( \frac{ - 2 + 4}{2} , \frac{ - 2+ 2}{2} )$

$( \frac{ 2}{2} , \frac{ 0}{2} )$

$( 1, 0)$

Using the second diagonals also gives,

$( \frac{ - 2 + 4}{2} , \frac{ - 3+ 3}{2} )$

$( \frac{ 2}{2} , \frac{ 0}{2} )$

$( 1, 0)$

Answer 2

HIJK is a parallelogram because the midpoint of both diagonals is (1,0)

which means they bisect each other.

Midpoint formula

This formula is used to calculate the midpoints of objects and is given

below:

(x₁+ x₂ /2 ), (y₁+y₂ / 2 )

The first diagonals are H(-2,2) and J(4,-2)

=(-2+4/2), (-2+2/2)

=(2/2, 0/2)

= (1,0)

The second diagonals also gives

=(-2+4/2), (-3+3/2)

=(2/2, 0/2)

= (1,0)

Hence the midpoint is (1,0).

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