Question

if the three points (-2,5),(2,2)and(a,-1)are collinear find the value of a​

Answer 1

Answer:

a = 6

Step-by-step explanation:

If the three points are collinear the area of triangle formed by joining the 3 points will be zero

Point A $(x_{1},y_{1})$ = (-2,5)

Point B $(x_{2},y_{2})$ = (2,2)

Point C $(x_{3},y_{3})$ = (a,-1)

Therefore,

$\frac{1}{2}|x_{1}(y_{2} - y_{3}) + x_{2}(y_{3} - y_{1}) +x_{3}(y_{1} - y_{2})| = 0\\ x_{1}(y_{2} - y_{3}) + x_{2}(y_{3} - y_{1}) +x_{3}(y_{1} - y_{2}) = 0\\-2(2 + 1) + 2(-1-5) + a(5-2) = 0\\(-2 * 3) + (2*-6) + (a*3) = 0\\-6 -12 + 3a = 0\\-18 + 3a = 0\\a = \frac{18}{3} = 6$

Therefore

a = 6 for the points to be collinear

Answer 2

Refer to the attachment.