PLEASE HELP! The vertices of square LMNO are L(0, 2), M(2, 0), N(0,−2), and O(−2, 0). Which of the following shows that its diagonals are congruent perpendicular bisectors of each other? I ATTACHED THE IMAGES.

The fourth one is correct.

Step-by-step explanation:

To show the diagonals are congruent, calculate their lengths using the Distance Formula: d=(x2−x1)2+(y2−y1)2‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾√.

Find the length of LN.

Substitute 0 for x1, 2 for y1, 0 for x2 and −2 for y2.

LN=(0−0)2+(−2−2)2‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾√

=02+(−4)2‾‾‾‾‾‾‾‾‾‾√

=8‾√

Find the length of MO.

Substitute 2 for x1, 0 for y1, −2 for x2 and 0 for y2.

MO=(−2−2)2+(0−0)2‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾√

=(−4)2+02‾‾‾‾‾‾‾‾‾‾√

=8‾√

Since LN=MO, by the definition of congruent line segments, LN=MO.

To show the diagonals are perpendicular, calculate their slopes using the Slope Formula: m=y2−y1x2−x1.

Find the slope of LN.

Substitute 0 for x1, 2 for y1, 0 for x2 and −2 for y2.

m1=−2−20−0=−40⇒m1 cannot be defined.

Find the slope of MO.

Substitute 2 for x1, 0 for y1, −2 for x2 and 0 for y2.

m2=0−0−2−2

=0−4

=0

The slope of LN cannot be defined, this means that LN is parallel to y-axis. The slope of MO is equal to 0, this means that MO is parallel to x-axis. x and y axis are perpendicular, therefore LN⊥MO.

The figure shows the same square L M N O on a Cartesian plane as in the beginning of the task. Diagonal L N is perpendicular to diagonal M O.

To show the diagonals bisect each other, calculate their midpoints using the Midpoint Formula: P(x1+x22,y1+y22).

Find the midpoint of LN.

Substitute 0 for x1, 2 for y1, 0 for x2 and −2 for y2.

P1(0+02,2+(−2)2)=(0, 0)

Find the midpoint of MO.

Substitute 2 for x1, 0 for y1, −2 for x2 and 0 for y2.

P2(2+(−2)2,0+02)=(0, 0)

Both midpoints are the same point on the coordinate plane. This means the two diagonals intersect at their midpoints, or bisect each other.

The figure shows the same square L M N O on a Cartesian plane as in the beginning of the task. The diagonals intersect at point P. Segments L P, P N, M P, and P O are congruent.

Therefore, the diagonals are congruent perpendicular bisectors of each other.

grab rope, tie a loop-de-loop, put it around ur neck, now jump while its tied to a high place. now your shoes are cool.

step-by-step explanation:

sas (side angle side)

aa(angle angle)

sss(side side side)

sas you have to find two sides with an angle in between

aa you find two angles because it will always add up to 180

sss find all sides

step-by-step explanation: