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| Distance Formula |
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| The length of the line segment AB, which joins A (x1, y1) and B (x2, y2) is given by |
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| Let A (x1, y1) and B (x2, y2) be two points in the plane. |
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| Let d = distance between the points A and B. |
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| Draw AL and BM perpendicular to x-axis (parallel to y-axis). |
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| Draw AC perpendicular to BM to cut BM at C. |
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| In the figure, |
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| OL = x1, OM = x2 [AC = LM = OM - OL = x2 - x1] |
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| MB = y2, MC = LA = y1 [CB = MB - MC = y2 - y1] |
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| From the right-angled DACB, |
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| Note: |
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| i) If the points A and B lie on the x-axis, then the ordinates of A and B are zeros. |
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| i.e., A (x1, 0), B (x2,0) |
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| ii) If the points A and B lie on the y-axis, then the abscissae of A and B are zeros. |
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| i.e., A (0,y1) and B (0,y2) |
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| iii) Distance of any point A (x, y) from the origin |
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| Example: |
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| Find the distance between the following pair of points: |
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| A (1,2) and B (4,5). |
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| Suggested answer: |
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| Using the distance formula, we have |
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