Question

P( h, 4) is the midpoint of line segment joining A (2, 5) and B (0, -3), then find h.​

Answer 1

Step-by-step explanation:

Given :-

( h, 4) is the midpoint of line segment joining A (2, 5) and B (0, -3).

Correction:-

B(0,3)

To find :-

Find the value of h ?

Solution :-

Given points are :

A (2, 5) and B (0, 3).

Let (x1, y1) = (2,5) => x1 = 2 and y1 = 5

Let (x2, y2) = (0,3) => x2 = 0 and y2 = 3

We know that

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

The mid point of the linesegment joining A and B = ( ( 2+0)/2 , (5+3)/2 )

=> Mid point = (2/2,8/2)

=> Mid point = (1,4) ----------(1)

According to the given problem

The mid point of AB = P(h,4) -------(2)

From (1)&(2)

=> (1) = (2)

=> (1,4) = (h,4)

=> (h,4) = (1,4)

On comparing both sides then

=> h = 1

Therefore, h = 1

Answer:-

The value of h for the given problem is 1

Used formulae:-

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

→ If (a,b) = (x,y) => a = x and b = y

Note :-

If A((2, 5) and B (0, -3). then

Mid point of AB = ( (2+0)/2 , (5-3)/2 )

=> (2/2, 2/2)

=> (1,1)

given that p(h,4)

So the y- coordinates of the both points are not equal .

So the point B must be equal to (0,3)