A teacher bought 12 packets of crayons. Seven of the packets had 9 crayons and the other 5 packets had 10 crayons. How many cray
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<u>Given</u>:
Given that the triangle ABC has vertices A(-2,3), B(0,3) and C(-1,-1).
We need to determine the coordinates of the image after a reflection over the x - axis.
Let A'B'C' denote the coordinates of the triangle after a reflection over the x - axis.
<u>Coordinates of the point A':</u>
The general rule to reflect the coordinate across the x - axis is given by
Substituting the point A(-2,3), we get;
Thus, the coordinates of the point A' is (-2,-3)
<u>Coordinates of the point B':</u>
The general rule to reflect the coordinate across the x - axis is given by
Substituting the point B(0,3), we get;
Thus, the coordinates of the point B' is (0,-3)
<u>Coordinates of the point C':</u>
The general rule to reflect the coordinate across the x - axis is given by
Substituting the point C(-1,-1), we get;
Thus, the coordinates of the point C' is (-1,1)
Hence, the coordinates of the image after a reflection over the x - axis is A'(-2,-3), B(0,-3) and C(-1,1)
Considering the definition of map and scale, an actual distance of 269.59 km represent a scale distance of 5.7 inches .
<h3>Definition of map and scale</h3>A map is a representation of a place, at a size smaller than the real size.
The scale of a cartographic representation is the relationship of similarity between the real dimensions of the geographical space represented and those of its image on the map. That is, the scale is defined as the proportionality relationship that exists between a distance measured on the ground and its corresponding measurement on the map.
One way to represent the scale is by a fraction, which indicates the proportion between the distance on a map and its corresponding distance in reality:
In this case, you know that a scale distance of 3.5 inches on a map represent an actual distance of 175 km.
To know the real distance that represents a scale distance of 5.7 inches, as the scale ratio is the same as in the previous case, it is expressed:
Solving:
×distance in reality= 5.7 inches
distance in reality=
<u><em>distance in reality= 269.59 km</em></u>
In summary, an actual distance of 269.59 km represent a scale distance of 5.7 inches .
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