Math Problem Statement

Three vertices of a square have coordinates A(2, 4), B(5, -1), and C(0, -4). Give the coordinates of the fourth vertex, D, in ordered pair (x, y) form.

Solution

To find the coordinates of the fourth vertex D(x,y)D(x, y) of the square, we use the geometric property that the diagonals of a square bisect each other at their midpoint and are perpendicular to each other.

Step-by-Step Solution:

  1. Determine the midpoint of diagonal AC: The midpoint of a line segment is given by: [ M = \left( \frac{x_1

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Math Problem Analysis

Mathematical Concepts

Coordinate Geometry
Properties of Squares

Formulas

Midpoint Formula: M = ((x1 + x2)/2, (y1 + y2)/2)
Slope Formula: m = (y2 - y1)/(x2 - x1)

Theorems

Diagonals of a Square Bisect Each Other and are Perpendicular

Suitable Grade Level

Grades 9-11

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