Question

Which lines are parallel based on the given points F(3, 3), K(6, 5), J(8, 2), and L(5, 0) in the coordinate plane?

A. Line enclosing F and K, and line enclosing K and J
B. Line enclosing F and K, and line enclosing L and J
C. Line enclosing L and J, and line enclosing L and K
D. Line enclosing F and K, and line enclosing J and J

Answer 1

The lines that are parallel based on the given points F(3, 3), K(6, 5), J(8, 2), and L(5, 0) in the coordinate plane are the line enclosing F and K, and the line enclosing L and J.

Step-by-step explanation:

The lines that are parallel based on the given points F(3, 3), K(6, 5), J(8, 2), and L(5, 0) in the coordinate plane are:

1. Line enclosing F and K
2. Line enclosing L and J

To determine if two lines are parallel, we need to find their slopes. If the slopes are equal, the lines are parallel. The slope of a line passing through two points (x1, y1) and (x2, y2) is given by the formula: slope = (y2 - y1) / (x2 - x1).

To find the slopes of the given lines:

• Line enclosing F and K: Slope = (5 - 3) / (6 - 3) = 2 / 3
• Line enclosing L and J: Slope = (2 - 0) / (8 - 5) = 2 / 3

Both lines have a slope of 2/3, so they are parallel.