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Coordinate Geometry
NCERT Exemplar
CBSE
Grade 10
Question:
The point which lies on the perpendicular bisector of the line segment joining the points $A(-2, -5)$ and $B(2, 5)$ is: (a) $(0, 0)$ (b) $(0, 2)$ (c) $(2, 0)$ (d) $(-2, 0)$
Step-by-Step Solution
Key Concept: The perpendicular bisector passes through the midpoint of the line segment and points equidistant from $A$ and $B$.
Midpoint of $AB = \left(\dfrac{-2 + 2}{2}, \dfrac{-5 + 5}{2}\right) = (0, 0)$. [0.5 Mark] Since $(0, 0)$ is the midpoint, it lies on the perpendicular bisector. [0.5 Mark]
--- 🎯 Official CBSE Marking Scheme: Calculating midpoint $(0, 0)$: 0.5 Mark Identifying that midpoint lies on perpendicular bisector: 0.5 Mark
Correct Answer:$(0, 0)$
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