Question

10. Determine whether MN and RS are parallel, perpendicular, or neither. M(-2, 2) N(1.-3) R(-2, 1) S(3,4)​

Answer 1

3.4 and 1 - 3

Explanation:

Answer 2

The relationship between line segments MN and RS is that they are perpendicular segments.

In Mathematics and Euclidean Geometry, two (2) lines are parallel under the following conditions:

Slope of line 1,
`m_1` = Slope of line 2,
`m_2`

Additionally, a condition that is true for two lines to be perpendicular is given by:

`m_1 * m_2 = -1`

Next, we would determine the slope of line segment MN and RS as follows;

`Slope(m)=(y_2-y_1)/(x_2-x_1)`

Slope (m) of MN = (-3 - 2)/(1 + 2)

Slope (m) of MN = -5/3

Slope (m) of MN = (4 - 1)/(3 + 2)

Slope (m) of MN = 3/5

Since the slopes are not the same, we can logically deduce that line segments are not parallel. However, the line segments are perpendicular because they are negative reciprocals of each other;

-5/3 × 3/5 = -1