The points (a, b+c), (b, c+a), and (c, a+b) are collinear.

To show that the points (a, b+c), (b, c+a), and (c, a+b) are collinear, we need to show that the slope between any two pairs of points is the same.

The slope between points (a, b+c) and (b, c+a) is:
m1 = (c+a - b) / (b - a) = (a+b - c) / (b - a)

The slope between points (b, c+a) and (c, a+b) is:
m2 = (a+b - c) / (c - b) = (b+c - a) / (c - b)

The slope between points (c, a+b) and (a, b+c) is:
m3 = (b+c - a) / (a - c) = (c+a - b) / (a - c)

Since m1 = m2 = m3, the points (a, b+c), (b, c+a), and (c, a+b) are collinear.

Given points are (a, b c), (b, c a), and (c, a b).

Let us plot these points on the graph.

The x-coordinates of the given points are a, b and c respectively.
The y-coordinates of the given points are b, c and a respectively.

Now, let us check whether the given points are collinear or not.
Three points are said to be collinear if they lie on the same straight line.

To check whether the given points are collinear or not, we will use the slope formula.
Slope formula is given by:
m = (y2 - y1) / (x2 - x1)

Let us calculate the slope between points (a, b c) and (b, c a).
m1 = (c - b) / (b - a)

Let us calculate the slope between points (b, c a) and (c, a b).
m2 = (a - c) / (c - b)

If m1 = m2, then the given points are collinear.

m1 = (c - b) / (b - a)
m2 = (a - c) / (c - b)
m1 = -m2

Therefore, the given points (a, b c), (b, c a), and (c, a b) are not collinear.

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