Question

The points A \( (-a, -b) \), B \( (0, 0) \), C \( (a, b) \) and D \( (a^2, ab) \) are

• A. collinear
• B. vertices of a parallelogram
• C. vertices of a square
• D. vertices of a rectangle

Hint:

To check if points are collinear, compute the slopes between pairs of points. If all slopes are equal, the points are collinear.

Answer 1

The Correct Option is A

Step 1: Understanding the coordinates.
The points are \( A(-a, -b) \), \( B(0, 0) \), \( C(a, b) \), and \( D(a^2, ab) \). To check if these points are collinear, we need to check if the slopes between pairs of points are equal. If the slopes between \( A, B \), \( B, C \), and \( C, D \) are all the same, the points are collinear. After calculating the slopes, we find that they are equal, so the points are collinear.

Step 2: Conclusion.
Thus, the correct answer is (A) collinear.