Solve the given problems. Sketch an appropriate figure,...

Solve the given problems. Sketch an appropriate figure, unless the figure is given.
Some of the streets of San Francisco are shown in Fig. 4.62. The distances between intersections $A$ and $B, A$ and $D,$ and $C$ and $E$ are shown. How far is it between intersections $C$ and $D ?$

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Key Concepts

Geometric Visualization

Constructing and interpreting a diagram is crucial in problems involving spatial relationships. Sketching the figure helps one understand the configuration of the intersections, streets, and the relative positions of points. This process aids in identifying which geometric principles, such as right triangles or parallel lines, may be applied to find unknown distances.

Distance Measurement and Coordinate Geometry

Calculating distances between points is a key concept in geometry. When points lie in a plane, techniques from coordinate geometry, such as using the distance formula or the concepts underlying the Pythagorean theorem, allow one to compute the length between two positions based on known segments or relationships within the diagram.

Pythagorean Theorem

The Pythagorean theorem is fundamental in determining the distance between two points in a right-angled configuration. By relating the lengths of the legs of a right triangle to its hypotenuse, this theorem provides a straightforward method to compute unknown distances when the geometry of the problem involves perpendicular intersections or right-angled components.

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