Line s passes through points (10, 7) and (3, 4). Line t passes through points (10, 4) and (3, 1). Are line s and line t parallel or perpendicular?
To determine if two lines are parallel or perpendicular, we can compare their slopes.
The slope of a line passing through two points $(x_1, y_1)$ and $(x_2, y_2)$ is given by the formula:
\[m = \dfrac{y_2-y_1}{x_2-x_1}\]
For line s passing through points (10, 7) and (3, 4), the slope is:
\[m_s = \dfrac{4-7}{3-10} = \dfrac{-3}{-7} = \dfrac{3}{7}\]
For line t passing through points (10, 4) and (3, 1), the slope is:
\[m_t = \dfrac{1-4}{3-10} = \dfrac{-3}{-7} = \dfrac{3}{7}\]
Since the slopes of line s and line t are equal, $m_s = m_t = \dfrac{3}{7}$, the lines are parallel.