Question

If P (9a – 2, –b) divides line segment joining A (3a + 1, –3) and B (8a, 5) in the ratio 3 : 1, find the values of a and bNCERT Class XMathematics - Exemplar ProblemsChapter _COORDINATE GEOMETRY

Answer 1

A ============P=============B
given
P (9a-2,-b)
A (3a+1,-3)
B (8a,5)
now use section formula for x -axis
9a-2={3 x 8a +1 x (3a+1)}/(3+1)
9a-2 =(24a+3a+1)/4
36a-8=27a+1
9a=9
a=1

again use section formula for y-axis
-b={3 x 5+1 x (-3)}/(3+1)
-4b=15-3
-4b=12
b=-3