Question

Find the value of k and show that the points (7,-2),(5,1), and (3,k) are collinear

Answer 1

Answer: k = 4

Step-by-step explanation:

1. When the points are colinear , the area of triangle =0
2. Given points are x1=7 , x2=5 , x3=3 , y1=-2 , y2=1 , y3=k
3. Area of triangle =0
4. 1/2[x1(y2-y3) + x2(y3-y1) + x3(y1-y2)] = 0
5. 1/2[7(1-k) +5(k+2) +3(-2-1)] =0
6. 7(1-k) + 5(k+2) + 3(-3) =0
7. 7-7k + 5k + 10 -9 =0
8. -7k +5k = -10+9-7
9. -2k = -8
10. 2k = 8
11. k = 8/2
12. k = 4