What is the area of the parallelogram whose vertices are listed? (0,0), (5,2), (6,4), (11,6)

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Aniqa O&#039;Neill · Accepted Answer

A parallelogram can be described with either four vertices or two vectors. In this case, since we are given four vertices (A, B, C, D), we can find vectors u and v that describe the parallelogram. graphing these points will show how the vectors are related.A=(0,0)B=(5,2)C=(6,4)D=(11,6)u=AB=[52]u=AC=[64]The area of a parallelogram is the magnitude of the determinant.[u1v1u2v2][u1v1u2v2]=det[5624]=20−12=8Result:8

Andre BalkonE · Accepted Answer

Step 1:First, we need to find the vectors AB→ and AD→ using the coordinates of points A, B, and D.The vector AB→ is obtained by subtracting the coordinates of point A from the coordinates of point B:AB→=(5−0,2−0)=(5,2).Similarly, the vector AD→ is obtained by subtracting the coordinates of point A from the coordinates of point D:AD→=(11−0,6−0)=(11,6).Step 2:Now, we can find the area of the parallelogram using the cross product of the vectors AB→ and AD→. The magnitude of the cross product gives us the area of the parallelogram:{Area}=|AB→×AD→|.The cross product of two vectors in 2D can be calculated as follows:AB→×AD→=(x1y2−x2y1), where x1 and y1 are the components of AB→ and x2 and y2 are the components of AD→.Applying the formula, we have:AB→×AD→=(5·6−11·2)=(30−22)=8.Taking the absolute value, we find that the area of the parallelogram is 8 square units.

Jazz Frenia · Accepted Answer

Result:8Solution:A=|𝐚×𝐛| where 𝐚 and 𝐛 are vectors formed by two adjacent sides of the parallelogram, and × denotes the cross product.Let&#039;s denote the given vertices as A(0,0), B(5,2), C(6,4), and D(11,6). We need to find the vectors 𝐚 and 𝐛.The vector 𝐚 is formed by the sides AB→ or DC→, and the vector 𝐛 is formed by the sides BC→ or AD→.Using the coordinates, we can find the vectors AB→ and BC→:AB→=⟨xB−xA,yB−yA⟩=⟨5−0,2−0⟩=⟨5,2⟩BC→=⟨xC−xB,yC−yB⟩=⟨6−5,4−2⟩=⟨1,2⟩Now, we can calculate the cross product of 𝐚 and 𝐛:𝐚×𝐛=|𝐢𝐣𝐤520120|Expanding the determinant, we have:𝐚×𝐛=(2·0−0·2)𝐢−(5·0−0·1)𝐣+(5·2−1·2)𝐤Simplifying further, we get:𝐚×𝐛=0𝐢−0𝐣+8𝐤=⟨0,0,8⟩Finally, we can find the magnitude of 𝐚×𝐛 to obtain the area of the parallelogram:A=|𝐚×𝐛|=|⟨0,0,8⟩|=02+02+82=64=8Therefore, the area of the parallelogram is 8 square units.

fudzisako · Accepted Answer

To find the area of a parallelogram given its vertices, we can use the formula:Area=|x1y2−x2y1+x2y3−x3y2+x3y4−x4y3+x4y1−x1y42|where (x1,y1), (x2,y2), (x3,y3), and (x4,y4) are the coordinates of the vertices.For the given vertices: (0,0), (5,2), (6,4), and (11,6), we can substitute the coordinates into the formula:Area=|(0·2−5·0+5·4−6·2+6·6−11·4+11·0−0·6)2|Simplifying this expression, we get:Area=|0+20−12+36−44+0−02|Area=|02|Therefore, the area of the parallelogram is 0 square units.

Find the area of the parallelogram whose vertices are listed. (0,0), (5,2), (6,4

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