
### Instruction: help me answer this question By using the concept of equation of a line, prove that the three points (3, 0), (– 2, – 2) and (8, 2) are collinear., think step by step
### Assistant: Collinearity of points can be proved by showing that the line passing through any two points also passes through the third point. Here, we have used the formula to find the equation of a line passing through two points and then checked if the third point also satisfies the equation of the line. , The answer is According to the question, if we have to prove that the given three points (3, 0), (– 2, – 2) and (8, 2) are collinear, then we have to also prove that the line passing through the points (3, 0) and (– 2, – 2) also passes through the point (8, 2). By using the formula, the equation of the line passing through the points (x1, y1) and (x2, y2) is given by -5y = -2(x – 3). Further simplifying the equation, we get 2x – 5y = 6. If 2x – 5y = 6 passes through (8, 2), then 2x – 5y = 2(8) – 5(2) = 16 – 10 = 6 = RHS. Hence, the line passing through the points (3, 0) and (– 2, – 2) also passes through the point (8, 2).
