Determine whether the three points are collinear. \( (0,-3),(-3,-8),(2,1) \) Are the three points collinear? Yes

To determine if the points \( (0,-3) \), \( (-3,-8) \), and \( (2,1) \) are collinear, we can use the area of the triangle formed by these points. If the area is zero, the points are collinear. The formula for the area \( A \) of a triangle given by points \( (x_1,y_1), (x_2,y_2), (x_3,y_3) \) is: \[ A = \frac{1}{2} \left| x_1(y_2 - y_3) + x_2(y_3 - y_1) + x_3(y_1 - y_2) \right| \] Plugging in the values: \[ A = \frac{1}{2} \left| 0(-8 - 1) + (-3)(1 + 3) + 2(-3 + 8) \right| = \frac{1}{2} \left| 0 -12 + 10 \right| = \frac{1}{2} \left| -2 \right| = 1 \] Since the area is not zero, the points are not collinear. If you love numbers and geometry, consider experimenting with graphing these points on a coordinate plane! Visualizing them can often help clear up whether they line up nicely or not. Plus, it’s a fun way to practice plotting points and understanding slopes. For those intrigued by geometry, delving into the concepts of slopes and equations of lines can be fascinating! You might want to check out the relationship between lines in algebra — understanding how slope can determine if points are collinear will enhance your math journey. Grab a graphing tool or app, and see for yourself!