Question

if the points p(-3 9) q(a b) and r(4 -5) are colinear and a+b=1 find the values of a and b

Answer 1

Answer:

According to the question given points p, q and r are collinear so area of triangle formed by joining p ,q and r will be equal to zero.

So

$\frac{1}{2 } | - 3(b + 5) + a( - 5 - 9) + 4(9 - b)| = 0 \\ \implies | - 3b - 15 - 14a + 36 - 4b| = 0 \\ \implies - 14a - 7b + 21 = 0 \\ \implies2a + b = 3................(i)$

also given that

a + b = 1.......(ii)

On solving (i)&(ii)

simultaneously we get

a= 2 and b = -1.

show Value of a and b will be 2 & -1 respectively.