Answer:

The figure is not a square, because:

The diagonals DO NOT intersect at their midpoints.

The diagonals are NOT of the same length.

The diagonals are NOT perpendicular.

Step-by-step explanation:

✍️If two diagonals intersect at their midpoints, the coordinates of their midpoints will be the same.

Find the midpoints of diagonal AC and BD using the midpoint formula, .

Midpoint (M) of AC, for A(-4, -6) and C(6, -18):

Midpoint of diagonal AC = (1, 12)

Midpoint (M) of BD, for B(-12, -12) and D(13, -1):

Midpoint of diagonal BD =

The coordinates of the midpoint of diagonal AC and diagonal BD are not the same, therefore, the diagonals do not intersect at their midpoints.

✍️Use distance formula to calculate the length of each diagonal to determine whether they are of the same length.

Distance between A(-4, -6) and C(6, -18):

(nearest tenth)

Distance between B(-12, -12) and D(13, -1):

(nearest tenth)

Diagonal AC and BD are not of the same length.

✍️If the diagonals are perpendicular, the product of their slope would equal -1.

Slope of diagonal AC:

A(-4, -6) and C(6, -18)

Slope of diagonal BD:

B(-12, -12) and D(13, -1)

Product of their slope:

The product of their slope doesn't equal -1. Therefore, diagonal AC and BD are not perpendicular to each other.