prove that through a given point, we can only draw one perpendicular to a given line.
Answers
Answer:
[Hint : Use proof by contradiction].
Step-by-step explanation:
From the point P , a perpendicular PM is drawn to the given line AB.
∴ ∠ PMB = 90
∘
Let if possible , we can draw another perpendicular PN to the line AB. Then ,
∠ PMB = 90
∘
∴ ∠ PMB = ∠ PNB , which is possible only when PM and PN coincide with each other.
Hence , through a given point , we can draw only one perpendicular to a given line.
solution
Answer:
Lets draw a line and mark a point such that does not lie on
Now lets draw a line perpendicular to from point .
Lets say we can draw another perpendicular line to through point
We know that the shortest distance of a point from a line is its perpendicular distance.
In other words, we can say that the shortest distance of a point from a line is a constant.
⇒
Applying the Pythagoras Theorem
We know that
⇒
⇒
⇒
Since, this means that the distance between the lines is zero.
This means that and coincide with each other.
∴ Through a given point, we can only draw one perpendicular to a given line.