Math Problem Statement

The diagram shows rectangle ABCD on a pair of axes. The lengths of its sides are 20 units and 5 units. The coordinates of point A are (3, 9). What are the coordinates of point C?

Solution

Let's break this down:

  1. Coordinates of Point C in the Rectangle:
    • The rectangle ABCD has the following known information:
      • Point A has the coordinates (3, 9).
      • The length of side AB is 20 units, and side BC is 5 units.
    • From the diagram, we can deduce the coordinates of point C:
      • Point A is at (3, 9).
      • Since side AB is horizontal (20 units), point B would be at (3 + 20, 9), i.e., at (23, 9).
      • Point C is vertically below point B (since side BC is 5 units), so the x-coordinate remains the same, but the y-coordinate is reduced by 5.
      • Therefore,

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Math Problem Analysis

Mathematical Concepts

Coordinate Geometry
Rectangle Geometry

Formulas

Distance formula
Properties of rectangles

Theorems

Parallel lines
Perpendicular lines
Properties of rectangles

Suitable Grade Level

Grades 6-8

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