Step-by-step explanation:
+) Polygons ABCD has: A(-7;4); B(-5;7); C(-3;4); D(-5; 1)
+) Polygons A'B'C'D' has: A'(-9;0); B'(-7;3); C'(-5;0); D'(-7;-3)
The side lengths of ABCD:
![AB = \sqrt{[-7-(-5)]^{2}+(4-7)^{2} } = \sqrt{13}](https://tex.z-dn.net/?f=AB%20%3D%20%5Csqrt%7B%5B-7-%28-5%29%5D%5E%7B2%7D%2B%284-7%29%5E%7B2%7D%20%20%7D%20%3D%20%5Csqrt%7B13%7D)
![BC = \sqrt{[-3-(-5)]^{2}+(7-4)^{2} } =\sqrt{13}](https://tex.z-dn.net/?f=BC%20%3D%20%5Csqrt%7B%5B-3-%28-5%29%5D%5E%7B2%7D%2B%287-4%29%5E%7B2%7D%20%20%7D%20%3D%5Csqrt%7B13%7D)
![CD = \sqrt{[-5-(-3)]^{2}+(1-4)^{2} } =\sqrt{13}](https://tex.z-dn.net/?f=CD%20%3D%20%5Csqrt%7B%5B-5-%28-3%29%5D%5E%7B2%7D%2B%281-4%29%5E%7B2%7D%20%20%7D%20%3D%5Csqrt%7B13%7D)
![DA = \sqrt{[-7-(-5)]^{2}+(4-1)^{2} } =\sqrt{13}](https://tex.z-dn.net/?f=DA%20%3D%20%5Csqrt%7B%5B-7-%28-5%29%5D%5E%7B2%7D%2B%284-1%29%5E%7B2%7D%20%20%7D%20%3D%5Csqrt%7B13%7D)
The side lengths of A'B'C'D':
![A'B' = \sqrt{[-7-(-9)]^{2}+(3-0)^{2} } = \sqrt{13}](https://tex.z-dn.net/?f=A%27B%27%20%3D%20%5Csqrt%7B%5B-7-%28-9%29%5D%5E%7B2%7D%2B%283-0%29%5E%7B2%7D%20%20%7D%20%3D%20%5Csqrt%7B13%7D)
![B'C' = \sqrt{[-5-(-7)]^{2}+(0-3)^{2} } =\sqrt{13}](https://tex.z-dn.net/?f=B%27C%27%20%3D%20%5Csqrt%7B%5B-5-%28-7%29%5D%5E%7B2%7D%2B%280-3%29%5E%7B2%7D%20%20%7D%20%3D%5Csqrt%7B13%7D)
![C'D' = \sqrt{[-7-(-5)]^{2}+(-3-0)^{2} } =\sqrt{13}](https://tex.z-dn.net/?f=C%27D%27%20%3D%20%5Csqrt%7B%5B-7-%28-5%29%5D%5E%7B2%7D%2B%28-3-0%29%5E%7B2%7D%20%20%7D%20%3D%5Csqrt%7B13%7D)
![D'A' = \sqrt{[-9-(-7)]^{2}+[0-(-3)]^{2} } =\sqrt{13}](https://tex.z-dn.net/?f=D%27A%27%20%3D%20%5Csqrt%7B%5B-9-%28-7%29%5D%5E%7B2%7D%2B%5B0-%28-3%29%5D%5E%7B2%7D%20%20%7D%20%3D%5Csqrt%7B13%7D)
So that side lengths of ABCD equal to those of A'B'C'D'.
However, this is not enough to said that they are congruent polygons, as 2 polygons are congruent when they have all corresponding sides and interior angles are congruent.
ABCD and A'B'C'D' have all corresponding sides congruent.
=> <em>So that "all corresponding interior angles are congruent" must be true for them to be congruent polygons</em>
There is no attached picture, but I guess it is like the one I attached.
If so, the first thing is finding the side measure:
Now, radius is half this measure: 15 in.
And circle area is:
Answer:
y=1/3
Step-by-step explanation:
3y+1=0
3y=-1
3y/3=-1/3
y=-1/3
Based on the calculations, the equation of this parabola is equal to (x - 6)² = 16(y + 4).
<h3>How to determine the equation of this parabola?</h3>
Mathematically, the standard equation with the vertex for a parabola is given by:
(y - k)² = 4a(x - h) for horizontal parabola.
(x - h)² = 4a(y - k) for vertical parabola.
<u>where:</u>
By critically observing the points, we can deduce that both the focus and vertex lie on the same vertical line x = 6.
<u>Given the following data:</u>
Focus with points = (6, 2).
Vertex (h, k) = (6, –4).
<u>Note:</u> a = 2 - (-4) = 2 + 4 = 6.
Substituting the given parameters into the formula, we have;
(x - 6)² = 4 × 4(y - (-4))
(x - 6)² = 16(y + 4).
Read more on parabola here: brainly.com/question/2346582
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