The quadrilateral with these following vertices is a parallelogram. (-4, -3), (2, -3), (4, -6), (-4, -6)

True
False

CLUE: The opposite sides of a parallel-

ogram are equal and parallel. Parallel
lines have equal slopes.

(-4,-3),(2,-3).
m1=(-3-(-3))/(2-(-4))=0
(L1)^2 = (2+4)^2 + (-3+3)^2 = 36,
L1=6.

(4,-6),(-4,-6).
m2 = (-6-(-6))/(-4-4) = 0.
(L2)^2 = (-4-4)^2 + (-6+6)^2 = 64,
L2 = 8.

This is not a parallelogram, because
the opposite sides are not equal.
This can also be proven graphically by
graphing the 4 points.

Given A (-6,4) and M(-1, -1) find B.

To determine if a quadrilateral is a parallelogram, we need to check if opposite sides are parallel.

Let's calculate the slopes of the two pairs of opposite sides.

The slope of a line passing through points (x1, y1) and (x2, y2) is given by (y2 - y1) / (x2 - x1).

The slopes of the sides are as follows:

1. Slope of side connecting (-4, -3) and (2, -3):
Slope = (-3 - (-3)) / (2 - (-4)) = 0 / 6 = 0

2. Slope of side connecting (2, -3) and (4, -6):
Slope = (-6 - (-3)) / (4 - 2) = -3 / 2 = -3/2

Since the slopes of these two sides are different (0 and -3/2), the opposite sides are not parallel.

Therefore, the quadrilateral with the given vertices is not a parallelogram.

Hence, the statement "False" is correct.

To determine whether the given quadrilateral is a parallelogram, we need to verify whether the opposite sides are congruent and the opposite angles are equal.

- Step 1: Find the length of each side of the quadrilateral using the distance formula:
The distance between two points (x1, y1) and (x2, y2) can be calculated using the formula: d = sqrt((x2 - x1)^2 + (y2 - y1)^2)
Let's calculate the distances of each side:

d1 = sqrt((2 - (-4))^2 + (-3 - (-3))^2) = sqrt(6^2 + 0^2) = sqrt(36 + 0) = sqrt(36) = 6
d2 = sqrt((4 - 2)^2 + (-6 - (-3))^2) = sqrt(2^2 + (-3)^2) = sqrt(4 + 9) = sqrt(13)
d3 = sqrt((-4 - 4)^2 + (-6 - (-6))^2) = sqrt((-8)^2 + 0^2) = sqrt(64 + 0) = sqrt(64) = 8
d4 = sqrt((-4 - (-4))^2 + (-6 - (-3))^2) = sqrt(0^2 + (-3)^2) = sqrt(0 + 9) = sqrt(9) = 3

- Step 2: Check if the opposite sides are congruent:
d1 = d3 = 6
d2 = d4 = 3

Since the opposite sides are congruent, we can move on to the next step.

- Step 3: Check if the opposite angles are equal:
To do this, we can calculate the slopes of the two pairs of opposite sides and check if they are equal.

The slope between two points (x1, y1) and (x2, y2) can be calculated using the formula: slope = (y2 - y1) / (x2 - x1)

Slope of side AB = (y2 - y1) / (x2 - x1) = (-3 - (-3)) / (2 - (-4)) = 0 / 6 = 0
Slope of side CD = (y2 - y1) / (x2 - x1) = (-6 - (-6)) / (4 - (-4)) = 0 / 8 = 0

Slope of side BC = (y2 - y1) / (x2 - x1) = (-6 - (-3)) / (4 - 2) = -3 / 2 = -1.5
Slope of side AD = (y2 - y1) / (x2 - x1) = (-6 - (-3)) / (-4 - (-4)) = -3 / 0
Since the slope of AD is undefined, we cannot compare it to the slope of BC.

Since the slopes of AB and CD are equal (0) and the slopes of AD and BC cannot be compared, we can conclude that the opposite angles are not necessarily equal.

- Step 4: Final Conclusion:
Since the opposite sides are congruent but the opposite angles are not necessarily equal, the given quadrilateral is not a parallelogram. Therefore, the answer is False.