Answer: x₁(y₂-y₃) + x₂(y₃-y₁) + x₃(y₁-y₂) = 0.
- A x₁(y₂-y₃) + x₂(y₃-y₁) + x₃(y₁-y₂) = 0
- B Their pairwise distances are all exactly equal
- C All three x-values are exactly equal to each other
- D The slopes between each pair of points are all positive
Correct answer: A. x₁(y₂-y₃) + x₂(y₃-y₁) + x₃(y₁-y₂) = 0
Explanation: Points are collinear iff area of triangle they form = 0. Area=(1/2)|x₁(y₂−y₃)+x₂(y₃−y₁)+x₃(y₁−y₂)|=0. Setting the determinant to zero gives the collinearity condition. Ans: x₁(y₂−y₃)+x₂(y₃−y₁)+x₃(y₁−y₂)=0.
The slope of a line is the ratio of vertical change (rise) to horizontal change (run) between any two points on it - equivalently, the tangent of the angle θ the line makes with the positive x-axis.