Question

If the points (k, 3), (2, 5) and (7, 9) are collinear, then the value of ’k’ is

Answer 1

Step-by-step explanation:

collinear means lying on same line

(x2 - x1) / (y2 - y1) = (x3 - x2)/( y3 - y2)

(2-k)/(5-3) = (7-2)/(9-5)

(2-k)/2 = 5/4

by cross multiplying

4(2-k) = 5*2

8 - 4k = 10

k= -1/2

please like my answer and mark as Brainliest

Answer 2

Answer:

• k = -1/2

Step-by-step explanation:

Given:

• (k, 3), (2, 5) and (7, 9) are collinear.

To Find:

• Find value of k.

$\implies {\bf We\;know\;that,}\\ \\ \\ \implies \sf \dfrac{1}{2}[x_{1}(y_{2}-y_{3}) +x_{2}(y_{3}-y_{1})+x_{3}(y_{1}-y_{2})]=0\\ \\ \\ \bf Where,\;x_{1}=k,\;x_{2}=2,\;x_{3}=7,\;y_{1}=3\;y_{2}=5,\;and\;y_{3}=9.\\ \\ \\ \implies \sf \dfrac{1}{2}[k(5-9)+2(9-3)+7(3-5)]=0\\ \\ \\ \implies \sf \dfrac{1}{2}[k(-4)+2(6)+7(-2)]=0\\ \\ \\ \implies \sf \dfrac{1}{2}[-4k+12-14]=0\\ \\ \\ \implies \sf \dfrac{1}{2}[-4k-2]=0\\ \\ \\ \implies \sf -4k=2\\ \\ \\ \implies \sf k = -\dfrac{1}{2}$

Hence, k = -1/2