Question

find the value of 'k' if the co-ordinates of the point A(2
,-2),B(-4,2),C(-7,k). are the collinear​

Answer 1

Step-by-step explanation:

Points are said to be colinear if they lie on the same straight line. This that the slopes of the lines joining any two of the points are the same.

So, if points (1, 4), (2, 7), and (3, k) are colinear, it means that the slopes of the lines joining points (1, 4) and (2, 7) or (1, 4) and (3, k) or (2, 7) and (3, k) are equal.

Recall that the slope ( m ) of the line joining two points ( x1,y1 ) and ( x2,y2 ) is given by m=y2−y1x2−x1 .

Then, the slope of the line joining points (1, 4) and (2, 7) is m1=7−42−1=3 .

Also, the slope of the line joining points (1, 4) and (3, k) is m2=k−43−1=k−42 .

Equating m1 and m2 , since the points are colinear, we have, k−42=3⇒k−4=2×3=6⇒k=6+4=10 .

Therefore, k=10 .

Answer 2

Answer:

x1=2,x2=-4,x3=-7

y1=-2,y2=2,y3=k

Step-by-step explanation:

area of the triangle = 1/2(x1(y2-y3)+x2(y3-y1)+x3(y1-y2))

0=1/2(2(2-k)+(-4)(k+2)+(-7)(-2-2))

0=1/2(4-2k-4k-8+28)

0=1/2(-6k+24)

0=-3k+12

3k=12

k=12/3

k=4