(2) Each question carries 2 marks. 1. Show that the points $$ A(-6,10), B(-4,6) $$ and $$ C(3,-8) $$ are collinear.

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To show that the points $$ A(-6,10), B(-4,6) $$ and $$ C(3,-8) $$ are collinear, we need to prove that the slope of the line segment $$ AB $$ is equal to the slope of the line segment $$ BC $$.

The slope of a line segment can be calculated using the formula:
$$ \text{Slope} = \frac{y_2 - y_1}{x_2 - x_1} $$

Let's calculate the slope of the line segment $$ AB $$ and the slope of the line segment $$ BC $$ to see if they are equal.
Calculate the value by following steps:
- step0: Calculate:
  $$\frac{\left(6-10\right)}{\left(-4+6\right)}$$
- step1: Remove the parentheses:
  $$\frac{6-10}{-4+6}$$
- step2: Subtract the numbers:
  $$\frac{-4}{-4+6}$$
- step3: Add the numbers:
  $$\frac{-4}{2}$$
- step4: Reduce the numbers:
  $$\frac{-2}{1}$$
- step5: Calculate:
  $$-2$$
The slope of the line segment $$ AB $$ is -2.

Now, let's calculate the slope of the line segment $$ BC $$.
Calculate the value by following steps:
- step0: Calculate:
  $$\frac{\left(-8-6\right)}{\left(3+4\right)}$$
- step1: Remove the parentheses:
  $$\frac{-8-6}{3+4}$$
- step2: Subtract the numbers:
  $$\frac{-14}{3+4}$$
- step3: Add the numbers:
  $$\frac{-14}{7}$$
- step4: Reduce the numbers:
  $$\frac{-2}{1}$$
- step5: Calculate:
  $$-2$$
The slope of the line segment $$ BC $$ is also -2.

Since the slope of the line segment $$ AB $$ is equal to the slope of the line segment $$ BC $$, the points $$ A(-6,10), B(-4,6) $$ and $$ C(3,-8) $$ are collinear.
The points $$ A(-6,10), B(-4,6) $$ and $$ C(3,-8) $$ are collinear because the slope of $$ AB $$ equals the slope of $$ BC $$.

(2) Each question carries 2 marks.

Show that the points and are collinear.

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(2) Each question carries 2 marks. Show that the points and are collinear.