The rule to describe this transformation is reflection
Explanation:
a. The line joining the midpoints of the parallel bases is perpendicular to both of them. It is the line of symmetry for the trapezoid. This means the angles and sides on one side of that line of symmetry are congruent to the corresponding angles and sides on the other side of the line. The diagonals are the same length.
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b. We observe that adjacent pairs of points have the same x-coordinate, so are on vertical lines, which have undefined slope. KN is a segment of the line x=1; LM is a segment of the line x=3. If the trapezoid is isosceles, the midpoints of these segments will be on a horizontal line. The midpoint of KN is at y=(3-2)/2 = 1/2. The midpoint of LM is at y=(1+0)/2 = 1/2. These points are on the same horizontal line, so the trapezoid <em>is isosceles</em>.
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c. We observed in part (b) that the parallel sides are KN and LM. The coordinate difference between K and L is (1, 3) -(3, 1) = (-2, 2). That is, segment KL is the hypotenuse of an isosceles right triangle with side lengths 2, so the lengths of KL and MN are both 2√2.
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For part (c), we used the shortcut that the hypotenuse of an isosceles right triangle is √2 times the leg length.
Yea that’s a nice graph i’d say looks a little fishy though
If you had values instead of algebraic expressions, you would find the area of the patio and subtract that from the area of the yard. Even though you don't have values, you can still find the area and subtract by expanding and simplifying:
(8x + 2)(6x + 3)
8x × 6x = 48x²
8x × 3 = 24x
2 × 6x = 12x
2 × 3 = 6
So you get 48x² + 36x + 6 as your area of the yard
(x + 5)(3x + 1)
x × 3x = 3x²
x × 1 = x
5 × 3x = 15x
5 × 1 = 5
So the area of the patio is 3x² + 16x + 5
(48x² + 36x + 6) - (3x² + 16x + 5)
48x² - 3x² = 45x²
36x - 16x = 20x
6 - 5 = 1
So your answer is D. 45x² + 20x + 1. I hope this helps!
Answer:
x=2
Step-by-step explanation: