Verify That the Points Are the Vertices of a Parallelogram $A ( 2,2,2 ) , B ( 3,4,5 ) , C ( 7,6,3 ) , D ( 8,8,6 )$

question 132

Multiple Choice

Verify that the points are the vertices of a parallelogram. $A ( 2,2,2 ) , B ( 3,4,5 ) , C ( 7,6,3 ) , D ( 8,8,6 )$

• A) \(\overrightarrow { A B } = ( 1,2,3 )\) is parallel to \(\overrightarrow { C D } = ( 1,2,3 )\)
• \(\overrightarrow { B D } = ( 1,4,5 )\) is parallel to \(\overrightarrow { A C } = ( 1,4,5 )\)
• Opposites are parallel and same length. So \(A B C D\) form a parallelogram.
• B) \(\overrightarrow { A B } = ( 1,2,3 )\) is parallel to \(\overrightarrow { C D } = ( 5,4,1 )\)
• \(\overrightarrow { B D } = ( 5,4,1 )\) is parallel to \(\overrightarrow { A C } = ( 1,2,3 )\)
• Opposites are parallel and same length. So \(A B C D\) form a parallelogram.
• C) \(\overrightarrow { A B } = ( 1,2,3 )\) is not parallel to \(\overrightarrow { C D } = ( 1,2,3 )\)
• \(\overrightarrow { B D } = ( 5,4,1 )\) is not parallel to \(\overrightarrow { A C } = ( 5,4,1 )\)
• Opposites are not parallel and same length. So \(A B C D\) form a parallelogram.
• D) \(\overrightarrow { A B } = ( 1,2,3 )\) is perpendicular to \(\overrightarrow { C D } = ( 1,2,3 )\)
• \(\overrightarrow { B D } = ( 5,4,1 )\) is perpendicular to \(\overrightarrow { A C } = ( 5,4,1 )\)
• Opposites are perpendicular and same length. So \(A B C D\) form a parallelogram .
• E) \(\overrightarrow { A B } = ( 1,2,3 )\) is parallel to \(\overrightarrow { C D } = ( 1,2,3 )\)
• \(\overrightarrow { B D } = ( 5,4,1 )\) is parallel to \(\overrightarrow { A C } = ( 5,4,1 )\)
• Opposites are parallel and same length. So \(A B C D\) form a parallelogram.

Assess the effect of activity level changes on total costs, net income, and cost per unit.

Estimate expected costs based on historical data using linear cost behavior assumptions.

Understand how to apply the high-low method to determine variable and fixed cost components.

Identify the nature of costs (fixed, variable, mixed, and step-variable) and their behaviors within relevant range.

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