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Example 4 - Three points P (h, k), Q (x1, y1), R (x2, y2) - Examples

  1. Chapter 10 Class 11 Straight Lines
  2. Serial order wise
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Example 4 Three points P (h, k), Q (x1, y1) and R (x2, y2) lie on a line. Show that (h – x1) (y2 – y1) = (k – y1) (x2 – x1). Since 3 points P, Q and R are collinear So, Slope of QP = Slope of RQ We know that slope of a line passing through (x1, y1)(x2, y2)is m = (𝑦_2 − 𝑦_1)/(𝑥_2 − 𝑥_1 ) Now, Slope of QP = Slope of RQ (𝑦_1 − 𝑘)/(𝑥_1 − ℎ) = (𝑦_2 − 𝑦_1)/(𝑥_2 − 𝑥_1 ) (k – y1) (x2 – x1) = (h – x1) (y2 – y1) (h – x1) (y2 – y1) = (k – y1) (x2 – x1) Hence proved

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Davneet Singh
Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He provides courses for Mathematics from Class 9 to 12. You can ask questions here.
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