Consider the effect of the transformation (x, y) → (x, 2y) on the parallelogram abcd with vertices a(0, 0), b(1, 1), c(3, 1), and d(2, 0). select true or false for each statement. a. the transformation preserves parallelism. a true b false b. the transformation preserves distance. a true b false c. the transformation preserves angle measure. a true b false

We have been given a transformation having rule

(x, y) → (x, 2y) on the parallelogram ABCD whose vertices are:

A(0, 0), B(1, 1), C(3, 1), and D(2, 0).

In given transformation x is same on both sides so x-coordinate will not change.

y changes to 2y so y-coordinate doubles. Due to that change in y, side length of the parallelogram will  change. Also the angle will change as you can see in the picture.

Now we can easily select True or False for each statement.

"The transformation preserves parallelism."

True

"The transformation preserves distance."

False

"The transformation preserves angle measure."

False

55.44 inches

step-by-step explanation:

part a. assuming a perfectly linear relationship, we can find the slope from the first two data points.

slope = m = (change in rainfall)/(change in years)

= (61.80 -62.33)/(2005 -2004) = -0.53/1 = -0.53

then the point-slope form of the equation of the line can be written as

y = m(x -h) +k . . . . . m = -0.53, (h, k) = (0, 62.33)

y = -0.53x +62.33 . . . x = years after 2004

part b. in 2017, x = 2017 -2004 = 13. then the predicted rainfall is

y = -0.53·13 +62.33 = 55.44 . . inches

the predicted rainfall in 2017 is 55.44 in.