Determine the scale factor used in the dilation of line segment AB , centered at the origin.
A(1,-3) -. B(2,-4)
A(4,-12) -> B(8,-16)
My apologies for the confusion in my previous responses. Let's correct the calculation of the fraction.
Starting with 283/100, we can simplify it by dividing both the numerator and the denominator by the greatest common divisor, which in this case is 1.
283 ÷ 1 = 283
100 ÷ 1 = 100
So, the simplified fraction for 283/100 is 283/100, which can be further simplified as:
283 ÷ 100 = 2.83
In decimal form, 283/100 is indeed 2.83. However, if you want to express this as a mixed number, you would have 2 with a remainder of 83/100. So, it can indeed be expressed as 2 83/100 or 2.83. Thank you for your patience, and I hope this clarifies the simplification.
The scale factor can be determined by comparing the length of the original line segment AB to the length of the dilated line segment AB.
Original line segment AB:
AB = sqrt((2-1)^2 + (-4-(-3))^2)
AB = sqrt(1^2 + 1^2)
AB = sqrt(2)
Dilated line segment AB:
AB' = sqrt((8-4)^2 + (-16-(-12))^2)
AB' = sqrt(4^2 + 4^2)
AB' = sqrt(32)
Scale Factor:
Scale factor = AB'/AB
Scale factor = sqrt(32)/sqrt(2)
Scale factor ≈ 2.83
Therefore, the scale factor used in the dilation of line segment AB centered at the origin is approximately 2.83.
Can you turn it into a fraction please?
Sure! To convert the decimal scale factor of approximately 2.83 into a fraction, we can first express it as a fraction with a denominator of 1:
2.83 = 2.83/1
Now, to convert 2.83 into a fraction, we need to invert the decimal part and add it to the whole number part:
2.83 = 2 + 0.83
2.83 = 2 + 83/100
Now, we can combine the whole number and fraction:
2.83 = 2 + 83/100
2.83 = 200/100 + 83/100
2.83 = (200 + 83) / 100
2.83 = 283 / 100
Therefore, the decimal scale factor of 2.83 can be expressed as a fraction 283/100.
Simplified version would be 1/4th right?
To simplify the fraction 283/100, we can divide both the numerator and the denominator by their greatest common divisor, which is 1.
283 ÷ 1 = 283
100 ÷ 1 = 100
Therefore, the simplified version of the fraction 283/100 is already in its simplest form: 283/100.
It is not equivalent to 1/4. The decimal 2.83 is equivalent to the fraction 283/100 but not to 1/4.