JAMIA 2021 — Mathematics PYQ
JAMIA | Mathematics | 2021The reflection of the point (α,β,γ) in the xy-plane is:
Choose the correct answer:
- A.
(α,β,0)
- B.
(0,0,γ)
- C.
(−α,−β,γ)
- D.
(α,β,−γ)
(Correct Answer)
(α,β,−γ)
Explanation
1. Point in 3D Space:
Let the given point be:
2. Reflection Rule for xy-plane:
When a point is reflected in the xy-plane, the x and y coordinates remain the same, but the z coordinate changes its sign (it becomes its additive inverse).
3. Transformation:
-
x coordinate: α→α
-
y coordinate: β→β
-
z coordinate: γ→−γ
Final Answer:
The reflection of the point (α,β,γ) in the xy-plane is:
Explanation
1. Point in 3D Space:
Let the given point be:
2. Reflection Rule for xy-plane:
When a point is reflected in the xy-plane, the x and y coordinates remain the same, but the z coordinate changes its sign (it becomes its additive inverse).
3. Transformation:
-
x coordinate: α→α
-
y coordinate: β→β
-
z coordinate: γ→−γ
Final Answer:
The reflection of the point (α,β,γ) in the xy-plane is: