Question

In what ratio the point (a,b) divides the line segment joining the points (a+b,b+a) and (a-b, b-a).

Answer 1

p_________Q_________R
(a+b,b+a) (a,b) (a-b,b-a)

X1=a+b. M1=m or M2=1
Y1=b+a
X=a
y=b
X2=a-b
Y2=b-a
Now let the ratio be m:1 .
we know that,
(X,Y)= {X1× M2+X2 ×M1÷ M1 + M2 , Y1×M2+Y2×M1÷M1 +M2}

(X,Y)= { (a+b) ×1 +(a-b)×m÷m+1,
(b-a)m + (b+a)1÷m+1 }

(a,b) ={ a+b +am -bm ÷m+1 ,bm-am +bm +am
÷m+1 }

or
a = a+b +am - bm ÷ m+1
am + a= a + b +am - bm
am - am + a - a= b - bm
b - bm = 0
- bm = -b
or
bm= b

and , m= 1
and ratio is 1:1

Answer 2

I hope it helps you dear!