A(1,2), B(3,-1), C(-1,-1). If ABCD is a parallelogram, find the coordinates of D.

April 7, 2026Mathematics

ScanSolve AI Answer

April 7, 2026

Answer

\left(\frac{x_A + x_C}{2}, \frac{y_A + y_C}{2}\right)$$

Here are the solutions to the problems:

a) (i) Find the coordinates of D Assuming ABCD is a parallelogram, the diagonals bisect each other. This means the midpoint of AC is the same as the midpoint of BD. Given points: $A(1,2)$ , $B(3,-1)$ , $C(-1,-1)$ . Let $D(x_D, y_D)$ .

Step 1: Find the midpoint of AC. $M_{AC} = \left(\frac{x_A + x_C}{2}, \frac{y_A + y_C}{2}\right)$

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a) (i) Find the coordinates of D Assuming ABCD is a parallelogram, the diagonals bisect each other.

Asked on April 7, 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 7, 2026

Here are the solutions to the problems: a) (i) Find the coordinates of D Assuming ABCD is a parallelogram, the diagonals bisect each other. This means the midpoint of AC is the same as the midpoint of BD. Given points: A(1,2), B(3,-1), C(-1,-1). Let D(x_D, y_D). Step 1: Find the midpoint of AC. M_AC = ((x_A + x_C)/(2), (y_A + y_C)/(2)) M_AC = ((1 + (-1))/(2), (2 + (-1))/(2)\