Question

"Are the points J(11, -2), K(3, -2), C(-5, 9), M(-6, -2) parallel, perpendicular, or neither in terms of their line segments?"

Answer 1

The line segments JK and KM are parallel because they have a slope of zero. However, segments JC and KM or JC and JK are neither parallel nor perpendicular as their slopes do not suggest such a relationship.

Step-by-step explanation:

To determine if the line segments formed by the points J(11, -2), K(3, -2), C(-5, 9), and M(-6, -2) are parallel, perpendicular, or neither, one can calculate the slope of each line segment, and compare them.

1. The slope of JK is calculated as (y2-y1)/(x2-x1). For points J(11, -2) and K(3, -2), the slope is (-2 - (-2)) / (3 - 11) = 0 / -8 = 0. A slope of zero indicates that JK is a horizontal line.
2. The slope of JC is ((9 - (-2)) / (-5 - 11) = 11 / -16, which is not zero or undefined, hence JC is neither horizontal nor vertical.
3. The slope of KM is ((-2 - (-2)) / (-6 - 3) = 0 / -9 = 0, showing that KM is also a horizontal line.
4. The slope of CJ is the negative reciprocal of JC, as (11 / 16), indicating they are not parallel or perpendicular.

From these calculations, segments JK and KM are parallel since they both have a slope of zero, meaning they are both horizontal lines. Segments JC and KM, or JC and JK, are neither parallel nor perpendicular since their slopes are not multiples of each other.