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3 years ago

15

How do you find the scale factor of a dilation?

2 answers:

Stolb23 [73]3 years ago

5 0

9514 1404 393

Answer:

scale factor = (image distance)/(pre-image distance)

Step-by-step explanation:

The scale factor from a pre-image to an image is the ratio of some linear measurement of the image to the corresponding linear measurement of the pre-image:

scale factor = (image distance)/(pre-image distance)

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The corresponding measurements can be measurements of side length, arc length, diameter, circumference, perimeter, chord length, or the length of any point on the image to the center of dilation (if known). The only requirement is that <em>corresponding measurements</em> be used, and that they be linear dimensions, not areas or volumes or angles (or anything else with units other than distance units).

lys-0071 [83]3 years ago

4 0

Answer:

To find the scale factor for a dilation, we find the center point of dilation and measure the distance from this center point to a point on the preimage and also the distance from the center point to a point on the image. The ratio of these distances gives us the scale factor

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The length of a rectangle is 6 more than twice the width. if the area is 40 cm^2, find the length and breadth of the rectangle

ra1l [238]

Answer: 3.217 & 12.434

Step-by-step explanation:

If we use <em>w</em> to represent the width, the length will be 6 more than 2 times w.

Hence, the length is $2w+6$ .

The area of a rectangle would be its length times its width, so let's make an equation to represent it's area.

$A=w(2w+6)$

We can also substitute 40 in for A as it's given in the question.

$40 = w(2w+6)$

Distributing <em>w</em> by multiplying it by both terms in the parentheses, we get

$40 = 2w^2+6w$

We can make the equation simpler by dividing both sides by 2.

$20 = w^2+3w$

Subtracting both sides by 20 will make the left-hand side 0.

$0=w^2+3w-20$

Now that we have put this <em>quadratic equation</em> into standard form (ax²+bx+c), we can find its solutions using the quadratic formula.

For reference, the quadratic formula is

$x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$

In this case, a is 1, b is 3, and c is -20.

Substituting, we get

$w=\frac{-3\pm\sqrt{3^2-4(1)(-20)}}{2(1)}$

$w= \frac{-3\pm\sqrt{9+80}}{2}$

$w=\frac{-3+\sqrt{89}}{2}\hspace{0.1cm}or\hspace{0.1cm}\frac{-3-\sqrt{89}}{2}$

Since the second solution results in a negative number, it cannot be the length of w.

$w=\frac{-3+\sqrt{89}}{2}\approx3.217$

The width/breadth of the rectangle is 3.217 cm.

To calculate the length, let's substitute the width into the expression for the length:

$l=2(3.217)+6$

$l=12.434$

The length of this rectangle is 12.434 cm.

6 0

1 year ago

10) what is the area ratio<br> 11) what is the area of RST <br> HELP ASAP EMERGENCY

dlinn [17]

9514 1404 393

Answer:

10) C 4/9

11) B 24

Step-by-step explanation:

10) The area ratio is the square of the ratio of side lengths. The ratio of side lengths is ...

RS/LM = 6/9 = 2/3

Then the area ratio is ...

(2/3)² = 4/9

__

11) Using the result of question 10, the area of ∆RST is ...

(4/9)(54 in²) = 24 in²

8 0

2 years ago

Meg has 15 marbles. Roberto has 3 times as many marbles as Meg. How many does Roberto have?

ValentinkaMS [17]

Answer:

Step-by-step explanation:

15*3=45

5 0

3 years ago

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Determine if the triangles are congruent.

spayn [35]

Answer:A

Step-by-step explanation:

7 0

2 years ago

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What is the volume of the figure?

RSB [31]

The answer is C hope this helps

4 0

3 years ago