Triangle ABC below is reflected across the y-axis and then translated 1 unit right and 2 units down.a) Write the coordinates of the vertices of the image after reflection.
b) Write a rule for the translation. Use arrow notation.
c) Write the coordinates of the vertices of the new image after translation.
Answers
Explanation:
When you reflect an image across the y-axis, it negates the x-coordinate. This means all of the x-coordinates will become the opposite sign after the reflection.
Since the translation is 1 unit right, that is adding 1 to the x-coordinate; since it is 2 units down, that is subtracting 2 from the y-coordinate. Once we add 1 to each x-coordinate and subtract 2 from each y-coordinate, we end up with the vertices listed above.
The coordinates of the vertices of the new image after translation and reflection :
A''(0, 1); B''(-3, 3); C''(-2, -1).
Further explanation
A reflection is an example of a transformation
Reflection is the process of mirroring each point on the geometry of a certain line.
The original figure is called the pre-image and the final figure is called the image
The image will be congruent with the pre image and the distance from the image to the mirror axis is the same as the distance from the pre image to the mirror axis
• The equation of reflection across the y-axis
x '= -x
y '= y
can be written
While the transformation itself is the displacement of the object given a distance and direction (for example up or down)
So each point is moved in the same distance and direction
Can be formulated :
A(x,y)⇒ T(a,b) ⇒ A'(x+a,y+b)(T=translated)
Triangle ABC below is reflected across the y-axis and then translated 1 unit right and 2 units down.
So the stages
1. reflected across the y-axis first and then
2. translated 1 unit right and 2 units down.(T(a,b) ⇒a=1,b=-2)
- reflected across the y-axis
Coordinate A(1,3),B(4,5),C(3,1)
reflected becomes :
A(1,3)⇒A'(-1,3)
B(4,5)⇒B'(-4,5)
C(3,1)⇒C'(-3,1)
- translated (T(a,b) ⇒a=1,b=-2)
A'(-1,3) ⇒A''(-1+1,3-2)⇒A"(0,1)
B'(-4,5) ⇒B''(-4+1,5-2)⇒A"(-3,3)
C'(-3,1) ⇒ C"(-3+1,1-2)⇒C"(-2,-1)
Learn more
Transformation from function
the rule for the reflection
the transformation rule
Keywords: reflection.,translation, the coordinates
Related Questions
Find the distance between points (3, 5) and (4, 6) to the nearest tenth.A) 3.2 B) 2 C) 2.8 D) 1.4
Find the square root of 7-2√5
Five less than three times the length L
One California fan palm tree grew 85 inches in 5 years. A queen palm tree grew 96 inches in 8 years. which tree grew faster? Explain.
Answers
Answer:
$3.33
Step-by-step explanation:
The costs listed are the cost for the total dinner (all 10 people). You need to add up all the costs, then divide by 10 to find the cost per person.
12.50 + 2.29 + 1.89 + 2.47 + 1.29 + 1.65 + 2.25 + 8.98 = 33.32
33.32 / 10 = 3.332
Rounded to the nearest cent, each serving costs $3.33.
Answer:
Hello there, you would multiply.
Step-by-step explanation:
You can't add by 10 if there are 10 more people, because all the ingredients would have to be timed
Answers
Answers
STEPS:
1) You place a decimal 2 digits from the end of the percent (or number)
2) You multiply the two numbers together
3) You find your answer
Answers
1/6÷3/1
1/6×1/3=
1/18
Answers
The jewelry store received 1,920 rings in the package that contain 1-inch cubes.
What is a cube?
It is a polygon having six faces.
The volume of a cube is side cube.
We have,
The package contains 1-inch cubes that each hold one ring, so the number of rings in the package is equal to the number of 1-inch cubes that can fit inside the package.
To find the number of 1-inch cubes that fit inside the package, we need to calculate the volume of the package in cubic inches.
The volume of a rectangular solid (such as a package) is given by the formula:
Volume = length x width x height
Plugging in the given values, we get:
Volume = 16 x 10 x 12
= 1,920 cubic inches
Since each 1-inch cube has a volume of 1 cubic inch, the number of cubes that can fit inside the package is equal to the volume of the package in cubic inches.
So,
Number of rings = 1,920
Thus,
The jewelry store received 1,920 rings in the package.
Learn more about cubes here:
#SPJ2
Answers
Answer:
1. Simply the left hand side by first multiplying the -12 with the (1-x) to get -12+12x since negative×negative will give you positive. So after the simplification on the left hand side you will get the expression 10-12+12x. Which will give you -2+12x on the left hand side.
2. You do same on the right hand side of the expression 8(-12+6x) -14. So you multiply the 8 with the expression in the bracket ONLY (-12+6x) then afterwards,you add the -14 it to get -96+48x-14 =-110+48x .NOTE. ADDING TO NEGATIVE NUMBERS GIVES YOU A NEGATIVE ANSWER. so -96+(-14)=-110. So after simplification. You will also get the expression-110+48x on the right hand side .
3. Then combining the two sides of the equation, the whole expression becomes
-2+12x = -110+48x. Then you group like terms by sending all number attached with a variable to the right hand side and non attached variable numbers to the left , given you
-2+110 = 48x-12x . NB .WHEN A POSITIVE NUMBER CROSSES THE EQUAL SIGN IT CHANGES TO NEGATIVE AND VICE VERSA.
4. -2+110 = 108 and 48x -12x =36x
So the final expression becomes 108= 36x
Then you divide both side by 36 ,thus 108÷36=36x÷36
Given you x= 3 as your final answer of the expression, since 108÷ 36= 3. And 36x÷36= x