Question

slope l1 =

1. l1: (2, 1) and (5, -7)

slope l1 =

1. l1: (1, 0) and (2, 0)

slope l1 =
slope l2 =
l2: (0, 0) and (-1, 2)
slope l2 =
l2: (5, -5) and (-10, -5)
slope l2 =
perpendicular
neither
parallel
perpendicular
neither
parallel
perpendicular
neither

Explanation:

Problem 3:

Step 1: Calculate Slope of L1

The slope formula is $m = \frac{y_2 - y_1}{x_2 - x_1}$. For L1 with points $(2, 1)$ and $(5, -7)$:
$m_{L1} = \frac{-7 - 1}{5 - 2} = \frac{-8}{3} = -\frac{8}{3}$

Step 2: Calculate Slope of L2

For L2 with points $(0, 0)$ and $(-1, 2)$:
$m_{L2} = \frac{2 - 0}{-1 - 0} = \frac{2}{-1} = -2$

Step 3: Determine Relationship

Two lines are parallel if their slopes are equal, and perpendicular if the product of their slopes is -1.
Product of slopes: $(-\frac{8}{3}) \times (-2) = \frac{16}{3}
eq -1$. Slopes are not equal. So, neither parallel nor perpendicular.

Step 1: Calculate Slope of L1

For L1 with points $(1, 0)$ and $(2, 0)$:
$m_{L1} = \frac{0 - 0}{2 - 1} = \frac{0}{1} = 0$

Step 2: Calculate Slope of L2

For L2 with points $(5, -5)$ and $(-10, -5)$:
$m_{L2} = \frac{-5 - (-5)}{-10 - 5} = \frac{0}{-15} = 0$

Step 3: Determine Relationship

Since both slopes are equal (0), the lines are parallel.

Answer:

Slope L1 = $-\frac{8}{3}$, Slope L2 = $-2$, Relationship: Neither

Problem 4: