Given P(1,-3); P'(-3,1) Q(3,-2);Q'(-2,3) R(3,-3);R'(-3,3) S(2,-4);S'(-4,2)
By observing the relationship between P and P', Q and Q',.... we note that (x,y)->(y,x) which corresponds to a single reflection about the line y=x. Alternatively, the same result may be obtained by first reflecting about the x-axis, then a positive (clockwise) rotation of 90 degrees, as follows: Sx(x,y)->(x,-y) [ reflection about x-axis ] R90(x,y)->(-y,x) [ positive rotation of 90 degrees ] combined or composite transformation R90. Sx (x,y)-> R90(x,-y) -> (y,x)
Similarly similar composite transformation may be obtained by a reflection about the y-axis, followed by a rotation of -90 (or 270) degrees, as follows: Sy(x,y)->(-x,y) R270(x,y)->(y,-x) => R270.Sy(x,y)->R270(-x,y)->(y,x)
So in summary, three ways have been presented to make the required transformation, two of which are composite transformations (sequence).
<span>The one-way ANOVA or one – way analysis of
variance is used to know whether there are statistically substantial
dissimilarities among the averages of three or more independent sets. It
compares the means between the sets that is being examined whether any of those
means are statistically pointedly dissimilar from each other. If it does have a
significant result, then the alternative hypothesis can be accepted and that
would mean that two sets are pointedly different from each other. The symbol, ∑
is a summation sign that drills us to sum the elements of a sequence. The
variable of summation is represented by an index that is placed under the
summation sign and is often embodied by i. The index is always equal to 1 and
adopt values beginning with the value on the right hand side of the equation
and finishing it with the value over head the summation sign.</span>
