I suspect 4/2 should actually be 4/3, since 4/2 = 2, while 4/3 would make V the volume of a sphere with radius r. But I'll stick with what's given:
In Mathematica, you can check this result via
D[4/2*Pi*r^3, r]
Geometry, please answer question ASAP
1 answer:
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By applying the equation of dilation, the coordinates of the vertices of the triangle ABC are A'(x, y) = (-12, 0), B'(x, y) = (0, -9) and C'(x, y) = (-12, -9).
<h3>How to find the image of a triangle</h3>
A dilation is a type of <em>rigid</em> transformation. <em>Rigid</em> transformations are transformations applied to <em>geometric</em> loci such that <em>Euclidean</em> distances are conserved.
There is a triangle and its image must be a triangle, the <em>new</em> triangle is found by transforming the three vertices of the prior one following this formula:
A'(x, y) = P(x, y) + k · [A(x, y) - P(x, y)] (1)
Where:
- P(x, y) - Center of reflection.
- A(x, y) - Original vertex
- A'(x, y) - New vertex
- k - Dilation factor
If we know that P(x, y) = (0, 0), A(x, y) = (-4, 0), B(x, y) = (0, -3) and C(x, y) = (-4, -3), then the new vertices of the triangle are, respectively:
Point A
A'(x, y) = (0, 0) + 3 · [(-4, 0) - (0, 0)]
A'(x, y) = (-12, 0)
Point B
B'(x, y) = (0, 0) + 3 · [(0, -3) - (0, 0)]
B'(x, y) = (0, -9)
Point C
C'(x, y) = (0, 0) + 3 · [(-4, -3) - (0, 0)]
C'(x, y) = (-12, -9)
Lastly, we draw the two triangles, which are presented in the image attached below.
To learn more on dilations: brainly.com/question/13176891
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