21. If the points A(k + 1, 2k), B(3k, 2k + 3) and C(5k - 1, 5k) are co

1.	21. If the points A(k + 1, 2k), B(3k, 2k + 3) and C(5k - 1, 5k) are collinear, thenfind the value of k
Answer» Given: If A (x1, y1) , B(x2, y2), C(x2,y2) To find: the value of k If three points are collinear then area of triangleABC = 0 1/2 { (x1[ y2-y1] +x2[y3-y1]+x3[y1-y2] } =0 given A(k+1,2k) ,B(3k,2k+3) ,C(5k-1,5k) therefore 1/2l(k+1)[2k+3-5k]+3k[5k-2k]+(5k-1)[2k-(2k+3)]l=0 (k+1)[3-3k]+3k*3k+(5k-1)(-3)=03k-3k²+3-3k+9k²-15k+3=06k²-15k+6=0 divide each term with 2 2k²-5k+2=02k²-4k-k+2=02k(k-2)-(k-2)=0(k-2)(2k-1)=0k-2 =- or 2k-1 =0 k=2 or k= 1/2 Like if you find it useful

21. If the points A(k + 1, 2k), B(3k, 2k + 3) and C(5k - 1, 5k) are collinear, thenfind the value of k

Answer»

Given:

If A (x1, y1) , B(x2, y2), C(x2,y2) To find: the value of k If three points are collinear then

area of triangleABC = 0

1/2 { (x1[ y2-y1] +x2[y3-y1]+x3[y1-y2] } =0

given A(k+1,2k) ,B(3k,2k+3) ,C(5k-1,5k)

therefore

1/2l(k+1)[2k+3-5k]+3k[5k-2k]+(5k-1)[2k-(2k+3)]l=0

(k+1)[3-3k]+3k*3k+(5k-1)(-3)=03k-3k²+3-3k+9k²-15k+3=06k²-15k+6=0

divide each term with 2

2k²-5k+2=02k²-4k-k+2=02k(k-2)-(k-2)=0(k-2)(2k-1)=0k-2 =- or 2k-1 =0

k=2 or k= 1/2

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