I had a question about a problem that I was working on for my pre-calculus...

flightwingsd2

flightwingsd2

Answered

2022-06-26

I had a question about a problem that I was working on for my pre-calculus class.

Here's the problem statement:

The area of the parallelogram with vertices 0, м , w , and v + w is 34. Find the area of the parallelogram with vertices 0, A v , A w , and A v + A w , where
A = ( 3 5 1 3 ) .
I got the answer by doing something very tedious. I set v = ( 17 0 ) and w = ( 0 2 ) , and did some really crazy matrix multiplication and a lot of plotting points of GeoGebra to get the answer of: 476 .

Now, I'm 100% sure that was not the fastest way, can someone tell me the non-bash way to do the problem?

Answer & Explanation

Angelo Murray

Angelo Murray

Expert

2022-06-27Added 23 answers

Hint: If v = ( a b ) and w = ( c d ) then the area of the original parallelogram is
| det ( a b c d ) | = | a d b c | .
Provide a similar expression for the area of the second parallelogram, and relate it to the above expression using properties of determinants.
sedeln5w

sedeln5w

Expert

2022-06-28Added 7 answers

You're probably supposed to know that the absolute value of the determinant of A is the area scale factor of the linear transformation represented by the matrix A. With this knowledge, you can easily solve the problem in your head.

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