Question

If R (x, y) is a point on the line segment joining the points P (a, b) and Q (b, a), then prove that x + y = a + b.

Answer 1

Step-by-step explanation:

can you please tell me only one co ordinate

Answer 2

x + y = a + b proved

Step-by-step explanation:

If R (x, y) is a point on the line segment joining the points P (a, b) and Q (b, a), then the 3 points are collinear. So the area of the triangle formed by the 3 points is zero.

 (1/2) [x1 (y2- y3 )+x2 (y3-y1 )+x3(y1-y2)] = 0  

 (1/2) [x (b-a)+ a (a - y) +b (y-b)] = 0  

  bx - ax + a² -ay +by - b² = 0

  a² - b² = ax + ay -bx - by

 (a+b) (a-b) = a (x+y) - b(x+y)

  (a+b) (a-b) = (a-b) (x+y)

Removing the common factor, we get:

 (a+b) = (x+y)

Hence proved.