Line c passes through points (10, 10) and (3, 2). Line d passes through points (10, 5) and (3, 13). Are line c and line d parallel or perpendicular?

Answer 1

To determine if lines c and d are parallel or perpendicular, we need to calculate the slopes of both lines.

The slope of a line passing through points (x1, y1) and (x2, y2) is given by the formula:

m = (y2 - y1) / (x2 - x1)

For line c passing through points (10, 10) and (3, 2):

m_c = (2 - 10) / (3 - 10)
m_c = -8 / -7
m_c = 8/7

For line d passing through points (10, 5) and (3, 13):

m_d = (13 - 5) / (3 - 10)
m_d = 8 / -7
m_d = -8/7

Since the slopes of lines c and d are negative reciprocals of each other, i.e. the product of the slopes is -1, the lines are perpendicular to each other.