Triangle RST was dilated by a scale factor of 1/2
Given: triangle R'S'T', is an isosceles triangle, with each leg measuring 8 units.
Pre-image:
measure of pre-image * scale factor = measure of resulting image
measure of pre-image = measure of resulting image / scale factor
measure of pre-image = 8 / 1/2
measure of pre-image = 8 * 2/1
measure of pre-image = 16 units.
Step-by-step explanation:
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).
We can divide this figure into triangle and trapezoid.
Area of a trapezoid = (1/2)*(base1 +base2)*height = (1/2)(11.75+18)*6.12 = 91.035
Area of a triangle = (1/2)*base*height=(1/2)*12*13.42 = 80.52
Area of the whole figure = 91.035 + 80.52 = 171.555
<h3>
Answer: 7/19</h3>
Explanation:
There are 7 blue marbles out of 4+7+8 = 11+8 = 19 total
The probability of selecting blue is therefore 7/19
We cannot reduce 7/19 any further because 7 and 19 have no common factors other than 1.
