Which graph shows a dilation? On a coordinate plane, 2 rectangles are shown. The larger rectangle is 8 units wide and 4 units hi
2 answers:
Answer:
The larger rectangle is 8 units wide and 4 units high. The smaller rectangle is 4 units wide and 2 units high
Step-by-step explanation:
we know that
A dilation is a non rigid transformation that produce similar figures
Remember that
If two figures are similar, then the ratio of its corresponding sides is proportional
therefore
If the graph shows a dilation. then the ratio of the corresponding sides of the figures must be proportional
we have
The larger rectangle is 8 units wide and 4 units high. The smaller rectangle is 4 units wide and 2 units high
The corresponding sides are
8 units wide and 4 units wide
4 units high and 2 units high
the ratio is
----> is true
so
The figures are similar
therefore
The graph show a dilation
The other options the corresponding sides are not proportional
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First of all, a bit of theory: since the area of a square is given by
where s is the length of the square. So, if we invert this function we have
.
Moreover, the diagonal of a square cuts the square in two isosceles right triangles, whose legs are the sides, so the diagonal is the hypothenuse and it can be found by
So, the diagonal is the side length, multiplied by the square root of 2.
With that being said, your function could be something like this:
double diagonalFromArea(double area) {
double side = Math.sqrt(area);
double diagonal = side * Math.sqrt(2);
return diagonal;
}