Question

line g passes through points (10, 3) and (1, 10). line h passes through points (9, 10) and (2, 1). are line g and line h parallel or perpendicular? parallel perpendicular neither

Explanation:

Step1: Calculate slope of line g

The slope formula is $m = \frac{y_2 - y_1}{x_2 - x_1}$. For line g with points (10, 3) and (1, 10), $m_g = \frac{10 - 3}{1 - 10} = \frac{7}{-9} = -\frac{7}{9}$.

Step2: Calculate slope of line h

For line h with points (9, 10) and (2, 1), $m_h = \frac{1 - 10}{2 - 9} = \frac{-9}{-7} = \frac{9}{7}$.

Step3: Check relationship

Two lines are perpendicular if the product of their slopes is -1. $m_g \times m_h = (-\frac{7}{9}) \times (\frac{9}{7}) = -1$. So they are perpendicular.

Answer:

perpendicular