In coordinate geometry, the reflection of a point in the origin means both its x-coordinate and y-coordinate change sign. What are the coordinates of the reflection of the point (3, -5) in the origin of the Cartesian plane?

Introduction / Context:
This question tests a basic coordinate-geometry transformation: reflection in the origin. Reflections are common in aptitude and analytic geometry, and the origin reflection is the simplest because it flips the point across both axes at the same time. The key idea is that the origin (0, 0) is the midpoint of a point and its image under this reflection.

Given Data / Assumptions:

• Original point P = (3, -5) • Reflection is taken in the origin (0, 0) • Required: coordinates of the reflected point

Concept / Approach:
Reflection in the origin maps any point (x, y) to (-x, -y). This happens because reflecting across the y-axis changes x to -x, and reflecting across the x-axis changes y to -y. Doing both together is exactly reflection through the origin.

Step-by-Step Solution:
1) Start with the rule for origin reflection: (x, y) → (-x, -y) 2) Identify x and y from the given point: x = 3 and y = -5 3) Change the sign of x: 3 becomes -3 4) Change the sign of y: -5 becomes 5 5) Therefore, the reflected point is: (-3, 5)

Verification / Alternative check:
Check using midpoint logic: The midpoint of (3, -5) and (-3, 5) is ((3 + -3)/2, (-5 + 5)/2) = (0, 0). Since the origin is the midpoint, this confirms it is a reflection through the origin.

Why Other Options Are Wrong:
• (3, 5): only y sign changes (reflection in x-axis, not origin). • (-3, -5): only x sign changes (reflection in y-axis, not origin). • (5, -3) and (-5, 3): these swap coordinates, which is a different transformation.

Common Pitfalls:
• Changing only one sign instead of both. • Swapping x and y (confusing reflection with rotation or interchange).

Final Answer:
(-3, 5)