Question

If the points (3,7), (1,k) and (-1,1) are collinear, what is the value of k?

Answer 1

`k=4`

Explanation:

`"the points are collinear thus lie in a line"`

`"since they are in a line then the slope between points"`
`"will be equal"`

`color(blue)"calculate slope between "(3,7)" and "(-1,1)`

`•color(white)(x)m=(y_2-y_1)/(x_2-x_1)larrcolor(blue)"gradient formula"`

`"let "(x_1,y_1)=(3,7)" and "(x_2,y_2)=(-1,1)`

`rArrm=(1-7)/(-1-3)=(-6)/(-4)=3/2`

`color(blue)"slope between "(3,7)" and "(1,k)=3/2`

`rArrm=(k-7)/(1-3)=(k-7)/(-2)`

`"equating and solving for k"`

`rArr(k-7)/(-2)=3/2`

`rArr2(k-7)=-6`

`rArr2k-14=-6`

`rArr2k=8rArrk=4`