70 POINTS! ∆ABC is reflected across the x-axis, then rotated 90° clockwise about the origin, and finally reflected across the line y = x to form ∆A′B′C′.The coordinates of vertex A′ are ____.
The coordinates of vertex B′ are ____ .
The coordinates of vertex C′ are ____.
Answers
Answer:
A'(1, 1); B'(3, 2); C'(1, 2)
Step-by-step explanation:
The original points are A(1,1 ), B(2, 3) and C(2, 1).
Reflecting the triangle across the x-axis will negate every y-coordinate; this maps
(1, 1)→(1, -1); (2, 3)→(2, -3); (2, 1)→(2, -1)
Rotating the figure 90° clockwise about the origin switches the x- and y-coordinates and negates the x-coordinate; this maps
(1, -1)→(-1 -1); (2, -3)→(-3, -2); (2, -1)→(-1, -2)
Reflecting across the line y=x will negate both the x- and y-coordinates; this maps
(-1, -1)→(1, 1); (-3, -2)→(3, 2); (-1, -2)→(1, 2)
Final answer:
To find the coordinates of ∆ABC after reflection across the x-axis, rotation by 90°, and reflection across y = x, we would apply these transformations to each point. Initially reflected across x-axis results in (x, -y), the 90° rotation gives (-y, x), and final reflection over y = x gives (x, -y). To find A′B′C′ we would need original coordinates, but general rule follows this pattern.
Explanation:
In this mathematics problem, we will find the coordinates for vertex A′, B′, and C′ of ∆A′B′C′. Given a triangle ∆ABC reflected across the x-axis, then rotated 90° clockwise about the origin, and finally reflected across the line y = x, we need the original coordinates of A, B, and C to find A′B′C′. However, if we take a generic point (x, y), we can assume the following:
- The reflection about the x-axis would turn it into (x, -y).
- The 90° clockwise rotation about the origin would give the new coordinates (-y, x).
- Finally, the reflection over the line y = x would change (-y, x) to (x, -y).
Assuming these transformations, we can find the final coordinates for A′, B′, and C′.
Learn more about Coordinate Transformations here:
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B. What is the balance after 2 years.
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=224.72
Answer:
A. $24
B. $224
Step-by-step explanation:
For simple interest, the formula is I = PRT where I = interest earned, P = principal amount borrowed/deposited, R = rate as a decimal, and T = time in years.
I = (200)(0.06)(2)
I = 24
Then add that to the amount deposited ($200) and you're done.
200 + 24 = $224
Please let me know if you have questions.
Who is correct?
Pattern: 18,26,34,42
A. Neither is correct. B. Both are correct. C. Only John is correct. D. Only Mary is correct.
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Yes, they are equivalent.
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Which calculation will give the total surface area of the cardboard, in square inches, that was used to make the box?
a
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b
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c
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