Geometry

# Collinearity

If three points $$A=(k,k+2),$$ $$B=(0,k-6)$$ and $$C=(k-4,k)$$ all lie on the same line, what is the value of $$k?$$

The $$x$$- and $$y$$-intercepts of a line have the same value. If the line passes through $$P=(7,-6)$$ and $$Q=(-6,k),$$ what is the value of $$k?$$

Consider the two points $$(-1, -1)$$ and $$(3, 7).$$ If a circle passes through these two points, then which of the following cannot also be a point on the circle?

What is the sum of all the values of $$k$$ that make three points $$A=(1,k),$$ $$B=(k,1)$$ and $$C=(10,10)$$ lie on the same line?

Consider the line passing through two points $$P=(1, 10)$$ and $$Q=(-1, 3)$$. If the line also passes through point $$R=(17, a)$$, what is the value of $$a$$?

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