The point (-4,1) is rotated 180 degrees counterclockwise using center (-3,0). What are the coordinates of the image?
2 answers:
Answer:
C. (-2, -1)
Step-by-step explanation:
It can help to plot the points.
For rotation 180 degrees, the center of rotation is the midpoint of the segment joining the given point and its image. That means you want to find the other end of a segment with one end (-4, 1) and midpoint (-3, 0).
For center of rotation O, this means ...
O = (A +A')/2
2O -A = A'
A' = 2(-3, 0) -(-4, 1) = (-6+4, 0 -1) = (-2, -1)
The coordinates of the image are (-2, -1).
You might be interested in
Using the z-distribution, it is found that since the p-value is less than 0.05, there is evidence to support the claim that the average cost of private universities are decreasing.
<h3>What are the hypothesis tested?</h3>At the null hypothesis, it is tested if the average cost is still of $50,000, that is:
At the alternative hypothesis, it is tested if the average cost is decreasing, that is:
The test statistic is:
In which:
is the sample mean.
is the value tested at the null hypothesis.
is the standard deviation of the population.
- n is the sample size.
The parameters for this problem are:
Hence:
z = -2.2.
<h3>What is the p-value and the conclusion?</h3>Using a z-distribution calculator, for a left-tailed test, as we are testing if the mean is less than a value, with z = -2.2, the p-value is of 0.0139.
Since the p-value is less than 0.05, there is evidence to support the claim that the average cost of private universities are decreasing.
More can be learned about the z-distribution at brainly.com/question/16313918
#SPJ1