Rectangle $ABCD$ABCD​ is translated and then reflected to create rectangle $A'B'C'D'$A′B′C′D′​ . Do rectangle $ABCD$ABCD​ and rectangle $A'B'C'D'$A′B′C′D′​ have the same area? Justify your answer.

Lipossig 2021-01-15 Answered
Rectangle $ABCD$ABCD​ is translated and then reflected to create rectangle $ABCD$A′B′C′D′​ . Do rectangle $ABCD$ABCD​ and rectangle $ABCD$A′B′C′D′​ have the same area? Justify your answer.
You can still ask an expert for help

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

Solve your problem for the price of one coffee

  • Available 24/7
  • Math expert for every subject
  • Pay only if we can solve it
Ask Question

Expert Answer

jlo2niT
Answered 2021-01-16 Author has 96 answers
When we translate the rectangle ABCD we do this by sliding the figure based on the transformation vector or directions of translations. When performing a translation we are sliding a given figure up, down, left or right. The orientation and size of the figure does not change. When applying the transformations we will transform each point and then redraw the figure.
when we reflect the rectangle we are just shifting the rectangle to the other side of either x or y axis (according to the reflection) at a distance equidistant from the axis. Hence each vertex shifts to a new position but remains at the same distance from the other vertex as previously before the reflection.
Hence there would be no change in the area of the rectangle if we translate and then reflect it.
Not exactly what you’re looking for?
Ask My Question

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

Relevant Questions

asked 2020-11-23

Consider the scatterplot of y versus x in Output B.6 above.
a. Which power transformations on y should be considered to straighten the scatterplot?
b. Which power transformations on x should be considered to straighten the scatterplot?
image

asked 2020-10-26
The ratio of the length (including the endzone) to the width of an NFL football field is 2.25. If the perimeter of the football field is 1040 feet, what are the dimensions of the field?
asked 2020-11-27
Starting with the function f(x)=ex, create a new function by performing the following transformations.
i. First shift the graph of f (x) to the left by two units.
f1(x)=?
ii. Then compress your result by a factor of 1/7
f2(x)= ?
iii. Next, reflect it across the x-axis.
f3(x)= ?
iv. And finally shift it up by eight units to create g (x).
g (x) =?
asked 2021-03-18

f(x)=13(x+1)+1
Domain and range?
Transformations?
Name of Graph?

asked 2021-02-05

Given f(x)=x2, after performing the following transformations: shift upward 58 units and shift 75 units to the right, the new function g(x)=

asked 2020-10-18
The garden is made up of a rectangular patch of grass and two semi-circular vegetable patches. If the dimensions of the rectangular patch are 16 m (length) and 8 m (width) respectively, calculate: a) the perimeter of the garden.
b) the total area of the garden.
asked 2020-11-22
Answer true or false to each of the following statements and explain your answers.
a. In using the method of transformations, we should only transform the predictor variable to straighten a scatterplot.
b. In using the method of transformations, a transformation of the predictor variable will change the conditional distribution of the response variable.
c. It is not always possible to fnd a power transformation of the response variable or the predictor variable (or both) that will straighten the scatterplot.