Answer:
A dilation with a scale factor of One-fourth and then a translation
Step-by-step explanation:
Plot points A, B, C, D, A', B, C' and D' on the coordinate plane and draw quadrilaterals ABCD and A'B'C'D'.
These quadrilaterals are similar and quadrilateral a'B'C'D' has sides 4 times smaller than quadrilateral ABCD.
This means that the dilation with a scale factor of one-fourth was performed.
The figures were not rotated (they have the same positions), so the second transformation was translation.
Hence, correct option is B: a dilation with a scale factor of One-fourth and then a translation
Sample Equation: 3x - 3 = 27
Multiple step:
3x - 3 = 27
<u> + 3 +3</u> Step1. Remove the -3 by adding 3 to both sides
3x = 30
<u>÷3 ÷ 3</u> Step2. Remove the multiplicand 3 by dividing both sides by 3
x = 10
To check: substitute x by its value
3x - 3 = 27
3(10) - 3 = 27
30 - 3 = 27
27 = 27
<h3>
Answer: (x-10)^2 + (y-1)^2 = 25</h3>
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Explanation:
The general template of a circle is
(x-h)^2 + (y-k)^2 = r^2
Where,
- (h,k) is the center
- r is the radius
We are given (10,1) as the center so (h,k) = (10,1) meaning that h = 10 and k = 1 pair up together.
r = 5 is the given radius.
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Plug the values h = 10, k = 1, r = 5 into the equation to get:
(x-h)^2 + (y-k)^2 = r^2
(x-10)^2 + (y-1)^2 = 5^2
(x-10)^2 + (y-1)^2 = 25
Answer:
<em>x = 17°, m∠ A = 114°</em>
Step-by-step explanation:
We can tell that these pair of angles are corresponding, provided;
Line 1 ║ Line 2, AB ∩ Line 1 and Line 2 ⇒ corresponding ∠s ≅,
m∠ A = m∠ B ⇒ Substitute values of A and B,
6x + 12 = 3x + 63 ⇒ Subtract 3x on either side,
3x + 12 = 63 ⇒ Subtract 12 on either side of equation,
3x = 51 ⇒ Divide either side by 3,
<em>x = 17 </em>⇒ Substitute value of x to solve for m∠ A,
m∠ A = 6 * ( 17 ) + 12,
m∠ A = 102 + 12,
<em>m∠ A = 114</em>
<em>Solution; x = 17°, m∠ A = 114°</em>
