Question

Use the diagram to answer the questions.

Is line m parallel to line n? Explain.


Is line m perpendicular to line k? Explain.

Answer 1

No

Yes

Explanation:

Let's find the inclination of the 3 lines.

m:

((-4) -3)/(0 - (-4))

-7/4

n:

((-2) -2)/(3 - 1)

-4/2

-2

k:

(1 -(-3)/(4 -(-3)

(1 +3)/4 +3

4/7

Okay, we find the inclination of all the three lines. For two lines be parallel, they have to have the same inclination. The inclination of m = -7/4 and the inclination of n = -2, so they're not parallel. And now, to know if m is perpendicular to k, they inclination have to be the opposite of the inverse of each other, so it means that they have to have opposite signals, and they need to be inverted fractions (for example a/b are inverted to b/a), and they are these two things: m = -7/4 and n = 4/7, so they're perpendicular

Answer 2

No, the slopes are not equal.

Yes, the slopes are negative reciprocals.

Explanation:

Just did it on edge.