Question

If P be the midpoint of AB. Coordinates of P& B are (3,1) & (5,-4), find A​

Answer 1

Step-by-step explanation:

Given:-

P be the midpoint of AB. Coordinates of P& B are (3,1) & (5,-4)

To find:-

Find the coordinates of the point A?

Solution:-

Let the coordinates of the point A be (x1, y1)

Coordinates of point B = (5,-4)

Let (x2, y2)=(5,-4)=>x2=5 and y2 = -4

We know that

The coordinates of mid point of the line segment joining the points A(x1, y1) and B(x2, y2) is

P(x,y) = ( {x1+x2}/2 ,{y1+y2}/2 )

=> P(x,y) = ( {x1+5}/2 ,{y1+(-4)}/2 )

=> P(x,y) = ( {x1+5}/2 , {y1-4}/2 )

According to the given problem

Mid point of the A and B = P(3,1)

=> ( {x1+5}/2 , {y1-4}/2 ) = (3,1)

On Comparing both sides then

=> (x1+5)/2 = 3 and (y1-4)/2 = 1

=> x1+5= 3×2 and y1-4 = 1×2

=> x1+5 = 6 and y1-4 = 2

=> x1=6-5 and y1 = 2+4

=> x1=1 and y1 = 6

A(x1, y1) = (1,6)

Answer:-

The coordinates of the point A = (1,6)

Used formula:-

The coordinates of mid point of the line segment joining the points A(x1, y1) and B(x2, y2) is

P(x,y) = ( {x1+x2}/2 ,{y1+y2}/2 ).