Answer:
The determinant is 15.
Step-by-step explanation:
You need to calculate the determinant of the given matrix.
1. Subtract column 3 multiplied by 3 from column 1 (C1=C1−(3)C3):
2. Subtract column 3 multiplied by 3 from column 2 (C2=C2−(3)C3):
3. Expand along the row 2: (See attached picture).
We get that the answer is 15. The determinant is 15.
9514 1404 393
Answer:
neither; they are the same distance from the line
Step-by-step explanation:
The distance of point (x, y) from line ax+by+c=0 is given by ...
d = |ax +by +c|/(√a² +b²)
Since we're using the same line for both points, we only need to evaluate ...
d = |ax +by +c|
Subtracting y can put the equation in the desired form:
1/2x -y +4 = 0
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For point A, the expression of interest evaluates to ...
|(1/2)(-2) -(6) +4| = |-1-6+4| = 3
For point B, the expression of interest evaluates to ...
|(1/2)(4) -(3) +4| = |2-3+4| = 3
These values tell us the points are the same distance from the line.
_____
The attached graph shows that circles of the same radius centered on A and B are both tangent to the line. Hence the distances are the same.
