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

1 Answer
Mar 17, 2018

#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#