The Magnification Equation is as follows:

The negative on the last part is very important. If you don't include it (and it's easy to forget), you will get the wrong answer.

We'll use the parts without  for our problem. We want , so we just need to multiply both sides by .

Now, we can plug in our numbers.

Therefore, the image height is . 

The magnification equation is 

where  is the height of the image, and  is the height of the object. We can plug these given values into the equation.

The magnification is a scalar value, so it's unitless. We can verify this by examining what goes into the equation. Both heights have the same units, which cancel, so that leaves us with no units.

The equation for magnification is

We're given the image distance and the magnification, so we'd use the second equality.

Now, we can plug in our numbers.

The negative in front of the equation is very important. If you forget it, the answer will be incorrect.

The distance from the mirror to the object is . Note that the object distance is always positive.

Using the relationship:

Where:

 is the object distance from the mirror

 is the image distance from the mirror

 is the focal length of the mirror

 is the radius of curvature of the mirror

Plugging in values:

Solving for :

Using the equation for magnification:

Where:

 is magnification

To determine magnification, we simply divide the object length from the image length. 

The negative sign is used to designate that the image is real. 

To solve this problem, it is essential to use the mirror equation:

Where:

 is the distance the object is from the mirror

 is the distance the image is from the mirror

 is the focal length of the mirror

To calculate the focal length, we'll have to use the radius of curvature:

Plugging this value into the top equation and rearranging, we obtain:

Therefore, the image distance is:

Since the image distance calculated above is a positive value, this means that the image forms on the same side of the mirror that the reflected light traveled. Thus, the image is real.

To determine whether the image is inverted or upright, we'll need to use the magnification equation:

The magnification obtained above is a negative number. As a result, the image formed from this scenario will be inverted.

Because we're dealing with a mirror, appropriately we would use the Mirror Equation:

where  is the focal length,  is the object distance, and  is the image distance. Because we're trying to solve for , we need to rearrange the equation to solve for it.

Now, we can just plug in our values for  and :

Therefore, the image distance is 13.1cm.

If you were to draw a line from an object to its image on a flat mirror, the line would be perpendicular to the plane of the mirror. The distance from the image to the mirror would be the same distance from the mirror to the object. Only point A fits both criteria, as all other points aren't perpendicular with the mirror, and point E isn't the same distance either.

For this problem, we use the mirror equation, rearraged to find .

 is the image location,  is the object location, and  is the focal point which is equal to the radius of curvature. Plugging in our known values:

Therefore, the image distance is  from the mirror. Remember, for concave mirrors, the image is on the same side as the object, and has a flipped orientation.

For convex mirrors, the mirror equation is slightly different than for concave mirrors.

Note the negative sign in front of the focal point. This is because a convex mirror is the same as a concave mirror pointing in the opposite direction.

Now, we rearrange the equation to solve for .

Now, we can plug in our numbers.

Therefore, the image is at , which is on the concave side of the mirror.