How does the operation of the pantograph relate to dilations and similarity? How can you use similar triangles to describe why the pantograph works as it does?

1.    The pin’s location aids to create two drawings simultaneously. This is that while drawing an image, a copy, which may vary in size, is created at the same time.

2.    The pantograph relates to dilation and similarity due to the use of similar triangles that affect the scale of the second drawing.  

3.    The use of similar triangles illustrates the process of the pantograph because the ratio of similitude is set when determining where to place the pin. When a triangle is moved while tracing a line, along with the outline of the image, an enlarged/reduced version of the image is created by the other pantograph's end.

4.    The pantograph is now obsolete and has been replaced by several different ways of producing duplicates such as photocopying, mass printing, and digital filing.

an individual’s sex (i.e., whether they are a male or female) is determined by the sex chromosomes. most people have two sex chromosomes, one that is inherited from their mother and one that is inherited from their father. typically, females have two x chromosomes (xx) and males have one x chromosome and one y chromosome (xy). conditions caused by changes (“mutations”) in genes located on the x chromosome are considered x-linked.

x-linked recessive inheritance

most x-linked conditions are recessive. this means that in a person with two x chromosomes (most females), both copies of a gene (i.e., one on each x chromosome) must have a change or mutation whereas in a person with one x chromosome (most males), only one copy of a gene must have a mutation. a female with a mutation in one copy of a gene on the x chromosome is said to be a “carrier” for an x-linked condition. a male with a mutation in a gene on the x chromosome is typically affected with the condition. because females have two copies of the x chromosome and males have only one x chromosome, x-linked recessive diseases are more common among males than females. however, x-linked recessive diseases can occur in both males and females.

for x-linked recessive disorders, an unaffected carrier mother who has a mutation in a gene on the x chromosome can transmit either the x chromosome with this mutation or a “normal” x chromosome to her children. if the father is unaffected, none of her daughters will be affected and all of her daughters will be unaffected—since they will inherit at least one normal x chromosome from their father. however, each daughter will have a 50% chance of being an unaffected carrier like her mother and a 50% chance of both x chromosomes being normal.