The points (2,4), (4,2), (7,1) are the vertices of:

The point  (2,4), (4,2), (7,1)

let the three points be A, B, and C

Here distance between AB

By using the distance formula

AB=$\sqrt{{(x_2-x_1)}^2+{(y_2-y_1)}^2}$

AB=$\sqrt{{(4-2)}^2+{(2-4)}^2}$

AB=$\sqrt{{\left(2\right)}^2+{\left(2\right)}^2}$

AB=$\sqrt{4+4}$

AB=$2\sqrt{2}$

Here distance between BC

By using the distance formula

BC=$\sqrt{{(4-7)}^2+{(2-1)}^2}$

BC=$\sqrt{{(-3)}^2+{\left(1\right)}^2}$

BC=$\sqrt{9+1}$

BC=$\sqrt{10}$

Here distance between AC

By using the distance formula

AC=$\sqrt{{(7-2)}^2+{(1-4)}^2}$

AC=$\sqrt{{\left(5\right)}^2+{(-3)}^2}$

AC=$\sqrt{25+9}$

AC=$\sqrt{34}$

Here all sides are different, Hence it is scalene triangle

The correct is option b.