9514 1404 393
1 cm : 1 m = 1/100
1 mm : 250 m = 1/250,000
exercise 6: (4, 0)
exercise 7: (-2, -4)
Step-by-step explanation:
Scales:
The scale factor can be written just as you show, with a simple modification. To make it a ratio, the usual replacements for the word "represents" are (a) a fraction bar (/), (b) a colon (:), or (c) the word "to", or (d) an equal sign (=).* That is, the scale could be written as any of ...
(1 cm)/(1 m) or 1 cm : 1 m or 1 cm to 1 m
However, if you want to write the scale as a fraction, you need to express both measures using the same units. Generally, the chosen units will be the smaller unit (1 m = 100 cm, for example, so the cm is the smaller unit).
Now, the ratios are (1 cm)/(100 cm) = 1/100. Note the units cancel, leaving only a number. Then the "unitless" ratio version is any of ...
1/100 or 1 : 100 or 1 to 100
All 6 of these forms can be called a "ratio." You would need to consult your curriculum materials to find out which form is intended by this question. (My personal preference is for the forms using a colon. We suspect the "unitless" version of the ratio is wanted here.)
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For the other one, we note that 1 m = 1000 mm, so the ratios could be ...
(1 mm)/(250 m) or 1 mm : 250 m or 1 mm to 250 m
1/250,000 or 1 : 250,000 or 1 to 250,000
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* I prefer to reserve an equal sign for situations where the left-side expression is actually equal to the right side expression. It is quite clear that 1 inch = 1 mile is a false statement when "equals" is taken literally. This preference comes from an early admonition by my Algebra teacher to "keep the equal sign sacred."
The attachment shows scales written using an equal sign and a fraction bar. Note the meaning of "small scale" and "large scale" is a reference to the relative size of the fraction. A fraction with a larger denominator is a smaller fraction. Where possible, a "unit fraction" (with a numerator of 1) is preferred.
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Translation Vectors
A translation vector is written by specifying the coordinates of the head (arrow end) relative to the tail. The delimiters (parentheses or other brackets) will need to match your curriculum materials. Sometimes angle brackets are used for vectors. As is usually the case, the coordinates are an ordered pair, with the horizontal distance first. Positive is taken to be right and up, so your vector will be of the form <right, up>, or (right, up).
Exercise 6:
4 units to the right is the translation vector (4, 0)
Exercise 7:
2 units left and 4 units down is the translation vector (-2, -4)
