Mathematics
A point P(a, b) become (-2, c) after reflection in the x-axis, and P becomes (d, 5) after reflection in the origin. Find the values of a, b, c and d.
Reflection
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Answer
We know that,
Rule to find reflection of a point in x-axis :
- Retain the abscissa i.e. x-coordinate.
- Change the sign of ordinate i.e. y-coordinate.
∴ Coordinates of point P(a, b) on reflection in x-axis is P'(a, -b).
According to question after reflection in x-axis P becomes (-2, c).
∴ (a, -b) = (-2, c) or,
⇒ a = -2
⇒ -b = c or b = -c.
We know that,
Rules to find the reflection of a point in the origin :
- Change the sign of abscissa i.e. x-coordinate.
- Change the sign of ordinate i.e. y-coordinate.
∴ Coordinates of point P(a, b) on reflection in origin is (-a, -b).
According to question after reflection in origin P becomes (d, 5).
∴ (-a, -b) = (d, 5) or,
⇒ -a = d or d = -(-2) = 2.
⇒ -b = 5 or b = -5.
Since, b = -c = -5, so, c = 5.
Hence, the value of a = -2, b = -5, c = 5 and d = 2.
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