Calculate the area of a parallelogram with corners in (-2,-1), (-12,-4), (9,-4), (-1,-7)?

Question

Jayden Jackson · Accepted Answer

Area #=63" "#square units

From the given points Let #A(x_a, y_a)=(-2, -1)# Let #B(x_b, y_b)=(-12, -4)# Let #C(x_c, y_c)=(-1, -7)# Let #D(x_d, y_d)=(9, -4)# The formula for polygons with points A, B, C, D is Area #=1/2[(x_a, x_b, x_c, x_d, x_a),(y_a, y_b, y_c, y_d,y_a)]# Area #=1/2[x_a*y_b+x_b*y_c+x_c*y_d+x_d*y_a-x_b*y_a-x_c*y_b-x_d*y_c-x_a*y_d]# Let use the formula Area #=1/2[(-2, -12, -1, 9, -2),(-1, -4, -7, -4, -1)]# Area #=1/2[(-2)(-4)+(-12)(-7)+(-1)(-4)+(9)(-1)-(-12)(-1)-(-1)(-4)-(9)(-7)-(-2)(-4)]# Area #=1/2[8+84+4-9-12-4+63-8]# Area #=1/2[159-33]# Area #=1/2[126]# Area #=63" "#square units God bless....I hope the explanation is useful.

Autumn Armstrong · Answer

undefined To calculate the area of a parallelogram given its corners, you can use the formula:

$$ \text{Area} = |(x_1y_2 + x_2y_3 + x_3y_4 + x_4y_1) - (y_1x_2 + y_2x_3 + y_3x_4 + y_4x_1)| $$

Given the coordinates of the corners:

$A(-2, -1)$, $B(-12, -4)$, $C(9, -4)$, $D(-1, -7)$

Substitute the coordinates into the formula:

$$ \text{Area} = |(-2 \times (-4) + (-12) \times (-4) + 9 \times (-7) + (-1) \times (-1)) - (-1 \times (-4) + (-4) \times 9 + (-4) \times (-1) + (-7) \times (-2))| $$

$$ \text{Area} = |(8 + 48 - 63 + 1) - (4 - 36 + 4 + 14)| $$

$$ \text{Area} = |(-6) - (-22)| $$

$$ \text{Area} = |16| $$

$$ \text{Area} = 16 $$

So, the area of the parallelogram is $16$ square units.

Violet Aldrich · Answer

undefined To calculate the area of a parallelogram with corners given by the coordinates (-2, -1), (-12, -4), (9, -4), and (-1, -7), you can use the formula for the area of a parallelogram formed by vectors. First, calculate the vectors between the opposite corners of the parallelogram:

Vector 1 = (x2 - x1, y2 - y1) = (-12 - (-2), -4 - (-1)) = (-10, -3)
Vector 2 = (x4 - x3, y4 - y3) = (-1 - 9, -7 - (-4)) = (-10, -3)

Next, find the cross product of these two vectors:
Cross product = (x1 * y2 - x2 * y1) = (-10 * -3) - (-10 * -3) = (-30 - (-30)) = 0

The magnitude of the cross product represents the area of the parallelogram formed by the vectors. Since the cross product is 0, it indicates that the parallelogram has no area, meaning that the points provided are not the corners of a parallelogram. Therefore, the area of the parallelogram cannot be calculated with the given coordinates.