Question

The midpoint of segment AB is P(0,4) if the coordinates of B are (-2,3) , then the coordinates of A are​

Answer 1

Answer:

(a) (2,5) Let (x, y) be the coordinates of A. then, Read more on Sarthaks.com - https://www.sarthaks.com/164797/the-midpoint-of-segment-ab-is-p-0-4-if-the-coordinates-of-b-are-2-3-then-the-coordinates-of-a-are

Answer 2

Step-by-step explanation:

Given:-

The midpoint of segment AB is P(0,4) and the coordinates of B are (-2,3) .

To find:-

Find the coordinates of A. ?

Solution:-

Let the coordinates of the point A be (x,y)

Coordinates of the point B ( -2,3) (given)

We know that

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

( { x1+x2)}/2 , {y1+y2}/2 )

Mid point of the line segment joining the points A(x,y) and B(-2,3)

=> ( { x+(-2) } /2 , {y+3}/2 )

=>( { x-2 } /2 , {y+3}/2 )

According to the given problem

The mid point of A and B = P(0,4)

=> ( { x-2 } /2 , {y+3}/2 ) = (0,4)

On Comparing both sides then

=> (x-2)/2 = 0 and (y+3)/2 = 4

=> x-2 = 0×2 and y+3 = 4×2

=> x-2 = 0 and y+3 = 8

=> x= 0+2 and y = 8-3

=> x = 2 and y = 5

=> (x,y) = (2,5)

The point A = (2,5)

Answer:-

The coordinates of the point A = (2,5)

Check:-

The coordinate of the mid point of the line segment joining the points (x1, y1) and (x2, y2) is ( { x1+x2)}/2 , {y1+y2}/2 )

Mid point of A and B

=>( (2-2)/2 , (3+5)/2 )

=> (0/2, 8/2)

=> (0,4)

Verified the given relation.

Used formula:-

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

( { x1+x2)}/2 , {y1+y2}/2 )