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20S Applied Math Mr. Knight – Killarney School Slide 1 Unit: Coordinate Geometry Lesson: CG-L2 Diagonal Distance Diagonal Distance Learning Outcome B-4 CG-L2 Objectives: To solve problems involving the calculation of diagonal distances.

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20S Applied Math Mr. Knight – Killarney School Slide 2 Unit: Coordinate Geometry Lesson: CG-L2 Diagonal Distance Not all distances between points are horizontal or vertical, as some may be diagonal. Going back to the previous lesson — to find the distance from the hospital to the hotel you would have to find the distance along a diagonal. To calculate the distance between two points on a diagonal, use the Pythagorean theorem. Theory – Diagonal Distance

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20S Applied Math Mr. Knight – Killarney School Slide 3 Unit: Coordinate Geometry Lesson: CG-L2 Diagonal Distance Find the distance, d, from the hospital to the hotel. Example 1

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20S Applied Math Mr. Knight – Killarney School Slide 4 Unit: Coordinate Geometry Lesson: CG-L2 Diagonal Distance The result can be summarized in this way: This relationship is commonly referred to as the Distance Formula. Pay careful attention to the subscripts. Mix them up, and your result will be incorrect. Theory – Distance Formula

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20S Applied Math Mr. Knight – Killarney School Slide 5 Unit: Coordinate Geometry Lesson: CG-L2 Diagonal Distance If the laundromat has coordinates (0, 0) and the hotel has coordinates (12, 2), use the distance formula to find the distance from the laundromat to the hotel in blocks. Example 2

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20S Applied Math Mr. Knight – Killarney School Slide 6 Unit: Coordinate Geometry Lesson: CG-L2 Diagonal Distance Find the distance between (-4, -2) and (1, 5). Example 3

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20S Applied Math Mr. Knight – Killarney School Slide 7 Unit: Coordinate Geometry Lesson: CG-L2 Diagonal Distance Example 4 Find the perimeter of the polygon shown below. The solution can be given to the nearest tenth.

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Proving the Distance Formula

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