Show that points A(-1, 1), B(p, p2), and C(1, 2p-1) are collinear.

April 11, 2026Mathematics

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April 11, 2026

Answer

(-1, 1)$

a) To show that the points $A(-1, 1)$ , $B(p, p^2)$ , and $C(1, 2p-1)$ are collinear, we can calculate the area of the triangle formed by these three points. If the area is zero, the points are collinear.

Step 1: Write down the coordinates of the points. $A(x_1, y_1) = (-1, 1)$ $B(x_2, y_2) = (p, p^2)$ $C(x_3, y_3) = (1, 2p-1)$

Step 2: Use the formula for the area of a triangle given its vertices.

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a) To show that the points A(-1, 1), B(p, p^2), and C(1, 2p-1) are collinear, we can calculate the area of the triangle formed by these three points.

Asked on April 11, 2026Mathematics

This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.

ScanSolve AI AnswerAnswered on April 11, 2026

a) To show that the points A(-1, 1), B(p, p^2), and C(1, 2p-1) are collinear, we can calculate the area of the triangle formed by these three points. If the area is zero, the points are collinear. Step 1: Write down the coordinates of the points. A(x_1, y_1) = (-1, 1) B(x_2, y_2) = (p, p^2) C(x_3, y_3) = (1, 2p-1) Step 2: Use the formula for the area of a triangle given its vertices. Area