Ex 7.1 Q10 - Find a relation between x and y such that the point (x, y) is equidistant from the point (3, 6) and (– 3, 4).
Solution:-Let, given points be A(x, y) , B(3, 6) and C(-3, 4)
➙ Since the point (x, y) is equidistant from the points (3, 6) and (-3, 4)
∴ AB = AC
∴ AB² = AC²
*Using distance formula
D² = (x₂-x₁)² + (y₂-y₁)²
∴ (x - 3)² + (y - 6)² = (x + 3)² + (y - 4)²
∴ x² - 6x + 9 + y² - 12y +36 = x² + 6x + 9 + y² - 8y + 16
∴ x² + y² - 6x - 12y + 45 = x² + y² + 6x -8y + 25
∴ -6x - 12y + 45 = 6x - 8y + 25
∴ 6x + 6x - 8y + 12y = 45 - 25
∴ 12x + 4y = 20
*Taking 4 as common
∴ 3x + y = 5
∴ 3x + y - 5 = 0
Hence,
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.
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Try This..
✒ Find the value of x for which the distance from (x, 5) to (1, –2) is 10 units.
✒ Show that the point (2, –1) lies on the perpendicular bisector of the line segment joining (3, 6) and (–3, 4).
✒ Find a relation between x and y such that the point (x, y) is equidistant from (4, –3) and (–2, 5).
❌ Common Mistakes
Forgetting to square both sides:▸ Always remove square roots by squaring both sides, a small mistake can lead to a completely wrong equation.Wrong expansion:▸ Watch out while expanding squares like . Don’t forget the middle term .Skipping simplification:▸ Students often leave the final equation without simplifying – aim for the neatest form!Cancelling incorrectly:▸ Only cancel like terms, especially on both sides of an equation. Double-check your signs!
📝 Related Questions:-
Queries Solved:-
Class 10 Ex 7.1
Ex 7.1 Q10 Class 10
Class 10 Ex 7.1 Q10
Class 10 Chap 7 Ex 7.1 Q10
Class 10 Coordinate Geometry
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