To find : The area of the parallelogram with the given vertices by using the determinant.
Thearea of the parallelogram is 10 square units.
Given information:
The vertices of the parallelogram are ( 0 , 0 ) , ( − 2 , 0 ) , ( 3 , 5 ) , ( 1 , 5 ) .
Formula used:
The area of the parallelogram with the vertices (0,0),( a , b ),( c , d ) and ( a + c , b + d ) is given by,
A = | det ( A ) |
Here, A = [ a b c d ]
Calculation:
It is given that the vertices of the parallelogram are ( 0 , 0 ) , ( − 2 , 0 ) , ( 3 , 5 ) , ( 1 , 5 ) .
Determine the area of the parallelogram as follows,
Consider ( − 2 , 0 ) = ( a , b ) and ( 3 , 5 ) = ( c , d ) .
A = [ − 2 0 3 5 ]
So, the area of the parallelogram is computed as,
A = | det [ − 2 0 3 5 ] | = | 5 ( − 2 ) − 3 ( 0 ) | = 10
Therefore, the area of the parallelogram is 10 square units.
Thearea of the parallelogram is 10 square units.
Given information:
The vertices of the parallelogram are
Formula used:
The area of the parallelogram with the vertices (0,0),( a , b ),( c , d ) and ( a + c , b + d ) is given by,
Here,
Calculation:
It is given that the vertices of the parallelogram are
Determine the area of the parallelogram as follows,
Consider
So, the area of the parallelogram is computed as,
Therefore, the area of the parallelogram is
Answer to Problem 21E
Thearea of the parallelogram is 10 square units.
Explanation of Solution
Given information:
The vertices of the parallelogram are
Formula used:
The area of the parallelogram with the vertices (0,0),( a , b ),( c , d ) and ( a + c , b + d ) is given by,
Here,
Calculation:
It is given that the vertices of the parallelogram are
Determine the area of the parallelogram as follows,
Consider
So, the area of the parallelogram is computed as,
Therefore, the area of the parallelogram is
Chapter 7 Solutions
PRECALCULUS W/LIMITS:GRAPH.APPROACH(HS)
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