What is the value of k?
2 answers:
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Step-by-step explanation:
The initial image of the photo is 2 in by 4 in. The mat is 4 in by 6 in.
The new image is dilated by a scale of 2. So we double the dimensions. The new photo is 4 in by 8 in. The new mat is 8 in by 12 in.
Answer:
The three positions are not on the same line.
Step-by-step explanation:
We have three points: A:(3,2,0), B:(1,-1,2) and C:(5,5,2).
Let's build a vector that goes from one point to another; that vector will be the director of a line (if we draw a vector that goes from A to B, that vector will be the direction of the line that pass by A and B because it does not change). In order to build that vector, let's subtract B from A:
The equation of a line is:
Where p is every singular point of the line, is a particular point of the line (any that we are sure that it is on the line), r is the director vector and t is the independent variable.
Now we have the director vector: (2,3,-2), and we can verify that A and B are on the line:
Because there is a value for t that satisfies both A and B: If we do and t=0, we are going to obtain the point p=A; and if we do t=-1, we are going to obtain p=B. Let's see that:
If C is also in the same line, C must accomplish the equation: , so:
Let's simplify the equation writing the parametric equation, which is just to write the equation for each dimension:
You can verify that there is not a value of t that satisfies all three equations, so, the point C is not on the same line as A and B; which means that A, B and C are not on the same line.