In circle M with m \angle LMN= 102m∠LMN=102 and LM=11LM=11 units find the of arc length of LN. Round to the nearest hundredth.

Given:

In a circle M with the measure of ∠LMN = 102° and LM = 11 units.

We need to determine the arc length of LN

Arc length of LN:

The arc length of LN can be determined using the formula,

where r is the radius and is the central angle.

Substituting and in the above formula, we get;

Simplifying, we get;

Rounding off to the nearest hundredth, we get;

Thus, the arc length of LN is 19.57 units.

First a more theoretical approach.

Suppose that we have a point (x, y), if you want to do a reflection over the y-axis, this point will transform into (-x, y).

This reflection leaves unchanged the distance between the point and the closest point to the axis of reflection.

Below, you can see a rough sketch of the situation.

Where the distance between the point S and the axis of reflection is 2 units, and the same for the distance between S' and the axis of reflection.

"Do you think you would see the same characteristic if you drew the line segment connecting T with the reflecting line and then T' with the reflecting line? How do you know?"

Yes, because as i wrote above, the distance between the point and the axis of reflection is invariant in this type of transformations.