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2 years ago

Determine if the two figures are congruent and explain your answer using transformations.

Mathematics

1 answer:

Maslowich2 years ago

7 0

The coordinate A(-1, 1) reflected over y-axis is (1, 1) is the coordinate of E, hence the two figures are congruent

The given figures are quadrilaterals, in order to determine whether they are similar, we need to check if they are reflections of each other.

For the Quadrilateral ABCD, the coordinate of A is at A(-1, 1) and for the Quadrilateral DEFG, the coordinate of E is at E(1, 1).

Note that if an object is reflected over the y-axis the transformation is (x, y)->(-x, y)

We need to check whether if we reflect the coordinate A over the y-axis we will get coordinate E

Since the coordinate A(-1, 1) reflected over y-axis is (1, 1) is the coordinate of E, hence the two figures are congruent

Learn more on reflections here:brainly.com/question/1908648

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Step-by-step explanation:

Let x be the length of rectangular plot and y be the breadth of rectangular plot

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2(x+y)=440

x+y=220

y=220-x

We are also given that an area of at least 8000 square feet.

So, $xy \leq 8000$

So, $x(220-x) \leq 8000$

$220x-x^2 \leq 8000$

So, $220x-x^2 = 8000\\-x^2+220x-8000=0$

General quadratic equation : $ax^2+bx+c=0$

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$x=\frac{-220 \pm \sqrt{220^2-4(-1)(-8000)}}{2(-1)}\\x=\frac{-220 + \sqrt{220^2-4(-1)(-8000)}}{2(-1)} , \frac{-220 - \sqrt{220^2-4(-1)(-8000)}}{2(-1)}\\x=45.96,174.031$

So, The possible parking lengths are 45.96 feet and 174.031 feet

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