Question

A3,5), B(2,-7) and C are the collinear points such that A-B-C and BA=AC Find the coordinates of C​

Answer 1

5/2, - 1 is the required answer

Answer 2

Answer:

Co-ordinate of point C = (4,17)

Step-by-step explanation:

As per the question,

Given three points A, B and C are collinear that means the given three points are in the same line.

Given data:

The co-ordinate of point A = (3,5)

The co-ordinate of point B = (2,-7)

and BA = CA .

Let us consider the co-ordinate of point C = (x,y)

As AB = AC that implies that point A is the midpoint of line BC.

Therefore, the x-coordinate of point A is half of the sum of the x-coordinates of point B and C and the y-coordinate of point A is half of the sum of the y-coordinates of point B and C.

∴ $3 =\frac{2+x}{2}$

          x = 4

And,

$5 =\frac{-7+y}{2}$

        y = 17

Co-ordinate of C = (x,y) = (4,17)

Hence, the co-ordinate of point C = (4,17)