Question

8. Assume that YZ is the perpendicular bisector of AB. 8a. Draw a diagram of this situation with point N labeled as the point of intersection. Be sure to properly label/notate the diagram with proper geometry markings. 8b. If AN is 3x and AB is 24, solve for “x”.

Answer 1

Since YZ is the perpendicular bisector of AB, we know that:

AN = NB = 3x (since YZ bisects AB)

AB = 24 (given)

We can also see from the diagram that the total length of AB is equal to the sum of AN and NB:

AB = AN + NB

Substituting in the values we know, we get:

24 = 3x + 3x

Combining like terms, we get:

24 = 6x

Dividing both sides by 6, we get:

x = 4

Therefore, the value of x is 4.

Answer 2

Assuming that YZ is the perpendicular bisector of AB, this means that YZ intersects AB at point N, and it does so at a right angle (perpendicular). how to draw it:

- Draw a line segment AB of length 24 units.
- Draw a line YZ that intersects AB at point N, and make sure that YZ is perpendicular to AB. This perpendicular bisector splits AB into two equal segments.

part 8b:

If AN is 3x, and AB is 24, we know that the perpendicular bisector YZ splits AB into two equal parts, so:

AN + BN = AB

Since AN is 3x, and AB is 24:

3x + BN = 24

Now, we need to solve for "x":

3x = 24 - BN

However, since YZ is the perpendicular bisector, BN is equal to AN (since they are both halves of AB):

3x = 24 - 3x

Now, we can solve for "x":

6x = 24

Divide both sides by 6:

x = 24 / 6

x = 4