NCERT Exemplar Solutions
Class 10 - Mathematics - CHAPTER 7: Coordinate Geometry - Exercise 7.1

Question 10

Step 1: Recall the property of the perpendicular bisector.
Any point on the perpendicular bisector of a line segment is equidistant from the two endpoints.

Step 2: Endpoints of the segment are given:
\(A(-2, -5)\) and \(B(2, 5)\).

Step 3: Check each option by finding the distance from the point to both A and B.
Distance formula: \[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \] (This is the standard Euclidean distance in the coordinate plane.)

Step 4: Try Option A \((0, 0)\).
Distance to A: \[ d(A, (0,0)) = \sqrt{(0 - (-2))^2 + (0 - (-5))^2} = \sqrt{(2)^2 + (5)^2} = \sqrt{4 + 25} = \sqrt{29} \] Distance to B: \[ d(B, (0,0)) = \sqrt{(0 - 2)^2 + (0 - 5)^2} = \sqrt{(-2)^2 + (-5)^2} = \sqrt{4 + 25} = \sqrt{29} \]

Step 5: Since both distances are equal (\(\sqrt{29}\)), point \((0,0)\) is equidistant from A and B. Hence, \((0,0)\) lies on the perpendicular bisector.

Step 6: The correct answer is Option A: (0,0).