Page 2
Solution: The distance between any two points can be measured using the distance formula which is given by √ [(x₂ - x₁)2 + (y₂ - y₁)2] Let point P (x, y) be equidistant from points A (3, 6) and B (- 3, 4). Since they are equidistant, PA = PB Hence by applying the distance formula for PA = PB, we get √(x - 3)² + (y - 6)² = √(x - (- 3))² + (y - 4)² √(x - 3)² + (y - 6)² = √(x + 3)² + (y - 4)² By squaring, we get PA2 = PB2 (x - 3)2 + (y - 6)2 = (x + 3)2 + (y - 4)2 x2 + 9 - 6x + y2 + 36 - 12y = x2 + 9 + 6x + y2 + 16 - 8y 6x + 6x + 12y - 8y = 36 - 16 [On further simplifying] 12x + 4y = 20 3x + y = 5 3x + y - 5 = 0 Thus, the relation between x and y is given by 3x + y - 5 = 0 ☛ Check: NCERT Solutions for Class 10 Maths Chapter 7 Video Solution: NCERT Class 10 Maths Solutions Chapter 7 Exercise 7.1 Question 10 Summary: The relation between x and y such that the point (x, y) is equidistant from the point (3, 6) and (- 3, 4) is 3x + y - 5 = 0. ☛ Related Questions:
Math worksheets and Open in App Suggest Corrections 20 If P (x , y ) is equidistant from the points A (7,1) and B (3,5) find the relation between x and y Let the point P(x, y) be equidistant from the points A(7, 1) and B(3, 5) Then PA = PB `⇒ PA^2 = PB^2` `⇒(x-7)^2 +(y-1)^2 = (x-3)^2 +(y-5)^2` `⇒ x^2 +y^2 -14x-2y +50 = x^2 +y^2 -6x -10y +34` `⇒ 8x -8y = 16 ` `⇒ x-y =2` Concept: Distance Formula Is there an error in this question or solution? |