Question

if R(x,y) is point is a point ont the line segment joining the P(a, b) and Q(b, a), then prove that x+y=a+b​

Answer 1

Depending on your question R may be the midpoint of seg P,Q

By midpoint formula

x = (x1 + x2)/2

x = (a + b)/2

and y = (y1 + y2)/2

y = (b + a)/2

$\tt \red{ now</p><p></p><p>,</p><p></p><p> }$

x + y = LHS

$\tt \: = \frac{a + b}{2} + \frac{b + a}{2} \\ \\ = \tt \frac{a + b + b + a}{2} \\ \\ \tt \: = \frac{2a + 2b}{2} \\ \\ \tt = \frac{2(a + b)}{2} \\ \\ \tt = a + b \\ \\ \tt a + b = RHS \\ \\ \tt \therefore \: x + y = a + b \\ \\ \: \tt \orange{Hence \: proved \: that, } \: \tt \downarrow \\ \tt \: \red{x + y = a + b}$