Question

3
3. If the coordinates of points A and B are (-2,-2) and (2, 4) respectively,
find the coordinates of the point P such that AP=AB, where P lies on
the line segment AB.
(CBSE 2015]
7​

Answer 1

Given : the coordinates of points A and B are (-2,-2) and (2, 4)

point P such that AP=AB, where P lies on the line segment AB

To Find : the coordinates of the point P

Solution:

coordinates of points A and B are (-2,-2) and (2, 4)

AP=AB, where P lies on the line segment AB

=> P is mid point of AB

Hence P = ( -2 + 2)/2  , ( -2 + 4)/2

=> P = (  0  , 1)

the coordinates of the point P are  ( 0 , 1)

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Answer 2

$\underline{\textbf{Given:}}$

$\textsf{The co ordinates of A and B are (-2,2) and (2,4) and P lies on}$

$\textsf{AB such that AP=AB}$

$\underline{\textbf{To find:}}$

$\textsf{The co ordinates of P}$

$\underline{\textbf{Solution:}}$

$\textsf{Let the co ordinates of P be (x,y)}$

$\textsf{Since P lies on AB and AP=AB,}$

$\textsf{we have A is the midpoint of BP}$

$\implies\mathsf{\left(\dfrac{2+x}{2},\dfrac{4+y}{2}\right)=(-2,-2)}$

$\implies\mathsf{\dfrac{2+x}{2}=-2\;\;\&\;\;\dfrac{4+y}{2}=-2}$

$\implies\mathsf{2+x=-4\;\;\&\;\;4+y=-4}$

$\implies\mathsf{x=-4-2\;\;\&\;\;y=-4-4}$

$\implies\mathsf{x=-6\;\;\&\;\;y=-8}$

$\therefore\underline{\textsf{The co ordinates of P are (-6,-8)}}$

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