if triangle ABC is rotated 180 degrees about the origin, what are the coordinates of A?
Answer:
The coordinates of A is [tex](-x_1,-y_1)[/tex].
Step-by-step explanation:
We are given that a triangle ABC is rotated 180 degrees about the origin .
We have to find the coordinates of A.
Let vertices of triangle ABC [tex]A(x_1,y_1),B(x_2,y_2) ,C(x_3,y_3)[/tex]
When we rotate the about 180 degrees then the coordinates changes like as
[tex](x,y)\rightarrow (-x,-y)[/tex]
When we rotate triangle ABC about 180 degrees then its vertices Ais ([tex]x_1,y_1)[/tex] change into [tex](-x_1,-y_1)[/tex]
Hence, the coordinates of A is [tex](-x_1,-y_1)[/tex].
Final answer:
After rotating triangle ABC 180 degrees about the origin, the coordinates of point A, initially at the origin (0, 0), remain unchanged at (0, 0).
Explanation:
If triangle ABC is rotated 180 degrees about the origin, the coordinates of point A after the rotation can be determined by applying the rules of rotation in the Cartesian coordinate system. Since point A is at the origin, its initial coordinates are (0,0). A rotation of 180 degrees about the origin will essentially reflect a point over both the x-axis and y-axis, but the location of point A will remain unchanged because it is located at the center of rotation. Therefore, the rotated coordinates of point A will still be (0, 0).
Two angles are complementary. If one angle measures 32 degrees, what is the measure of the second angle?
If one angle measures 32 degrees, the measure of the second angle can be found by subtracting 32 from 90. Therefore, the second angle is 58 degrees.
Explanation:Complementary angles are two angles whose sum is 90 degrees. So, if one angle measures 32 degrees, we can find the measure of the second angle by subtracting 32 from 90:
Second angle = 90 - 32
Second angle = 58 degrees
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Antoine is wrapping a block of cheese that is 22 centimeters long by 6 centimeters high by 10 centimeters wide with plastic wrap. What is the surface area of the cheese box?
The table shows the results of drawing letter tiles from a bag. What is the probability that the next title drawn will have the letter C on it?
Outcome. Number of times drawn
A. 12
B. 5
C. 18
D. 15
A) 1/18
B)6/25
C)9/25
D)18/25
Find the area of the figure
Billy is flying his new radio-controlled helicopter around town. He is using a map in which each grid line is equivalent to 100 feet. Billy releases the helicopter from the library parking lot, at (2, 6) on the map. He gets it to cruising altitude and then starts measuring its flight. Billy flies the helicopter in a direct line to the town pool, at (6, 9) on the map. How far has the helicopter flown?
The helicopter has flown a distance of 500 feet as calculated using the Euclidean distance formula for two points on a grid.
Explanation:To find the distance the helicopter has flown, we need to calculate the Euclidean distance between the two points (2,6) and (6,9) on the grid map. We can use the formula: Distance = √[(x₂ - x₁)² + (y₂ - y₁)²], where (x₁, y₁) and (x₂, y₂) are the coordinates of the two points. Substituting the given points into the formula, we have:
Distance = √[(6 - 2)² + (9 - 6)²] = √[(4)² + (3)²] = √[16 + 9] = √25 = 5 grid lines.
Given that each grid line is equivalent to 100 feet, the helicopter has traveled 5 grid lines * 100 feet/grid line = 500 feet.
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What is the slope of line m?
A.2
B.-2
C.-1/2
D.1/2
Hi there!
Step-by-step explanation:
Lesson: Exploring Slope/ and slope intercept formFirst, you use slope formula.
[tex]SLOPE=\frac{Y^2-Y^1}{X^2-X^1}=\frac{RISE}{RUN}[/tex]
[tex]\frac{(-4)-0=-4}{0-(-2)=0+2=2}=\frac{-4}{2}=\frac{-4/2}{2/2}=\frac{-2}{1}=-2[/tex]
Slope is -2
Answer is -2
*the answer must have a negative sign.*
I hope this helps you!
Thanks!
Have a nice day! :)
-Charlie
:D
The probability of Jaden making a free throw is 15%. Predict the number of free throws that he can expect to make if he attempts 40 free throws.
We have been given that the probability of Jaden making a free throw is 15%.
Now, we have to predict the number of free throws that he can expect to make if he attempts 40 free throws.
In order to find the total number of free throws, we will find 15% of 40.
Therefore, the number of free throws should be
[tex]15\% \text{ of }40\\ \\ =\frac{15\times 40}{100} \\ \\ =\frac{600}{100} \\ \\ =6[/tex]
Therefore, the number of free throws that he can expect to make if he attempts 40 free throws is 6.
the average car length is 200 inches. how many feet and inches is the average car
A father is ten times as old as his daughter. In 5 years he will be just five times as old as she will be. How old are they now? HELP PLEASEEE
The given problem is an algebraic equation where the daughter's age is denoted as 'x' and the father's age as '10x'. An equation is formulated to solve for 'x' based on future ages. The solution to the problem is that the daughter is 5 years old, and the father is 50 years old.
Explanation:The problem asked is a classic example of algebra problem solving. We are told that a father is 'ten times as old as his daughter', and in five years, 'he will be just five times as old as she will be'. Let's denote the daughter's current age as 'x'. Therefore, the father's current age will be '10x'.
In five years, the daughter will be 'x+5' and the father will be '10x+5'. At this future moment, the father is 'five times as old as the daughter', so we can create the equation: 10x + 5 = 5(x + 5). Solving this equation leads to 'x=5'. So, the daughter is 5 years old and the father is 50 years old.
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What is the attribute being measured?
A. Psi
B. Stress
C. glass rods
D. number of rods
Answer:
B. Stress
Step-by-step explanation:
Did the usa prept test :)
What expression can be used for estimating 868 divided by 28?
Pls help me
Thanks
Jason and Kyle both choose a number from 1 to 10 at random. What is the probability that both numbers are odd?
calculate length of x
given the function f(x)=2x^2-3x, calculate f(a+h)-f(a)/h
WILL MARK BRAINLIEST!!!
PLEASE JUST HELP!!!!
END OF UNIT ASSESSMENT TEST QUESTION!!!!
The table shows the results of a random survey of children between the ages of 10 and 15 about their favorite food.
Pizza Hamburger Chicken fingers Hot dogs Mac and cheese
67 42 59 14 24
Based on these results, if 375 children are asked about their favorite food, how many children will prefer pizza?
verify the identity sec(theta)sin(theta)cot(theta) = 1
Just say answer, no need to explain. Thanks
What is the axis of symmetry for
Y=5x^2+12x+2
Which choice represents the best rational approximation for *square root symbol* 3? A) 14/9 B) 15/13 C) 17/10 D) 6/5
A rational number is a number which is in the form [tex]\frac{p}{q} ,q \neq 0[/tex]
Now, the value of the number [tex]\sqrt 3 = 1.73[/tex]
Now let us evaluate each given rational number in decimal form.
[tex]\frac{14}{9} = 1.6\\ \\ \frac{15}{13} = 1.2\\ \\ \frac{17}{10} = 1.7\\ \\ \frac{6}{5} = 1.2[/tex]
Therefore, among these numbers, the best approximation is option c i.e. 17/10.
C is the correct option.
Answer:
C) [tex]\frac{17}{10}[/tex]
Step-by-step explanation:
[tex]1,732050808 ≈ \sqrt{3} \\ \\ 1,73 ≈ \sqrt{3}[/tex]
Therefore answer choice C) would be the best approximate answer to this:
* [tex]1\frac{7}{10} = 1,7[/tex]
I am joyous to assist you anytime.
mrs adrian bought 30 yards of dirt for her garden in her backyard. she hired 4 girls to spread the dirt if the girls divided the dirt up evenly, how many yards did each girl need to spread mrs adrians garden?
Use the above figure to answer the following questions. Show your work if possible
A. What is the intersection of plane P and plane R?
B. Name three points that are collinear
C. Name R in two more ways
D. Name four coplanar points
Help please Math Geometry
find the slope of, m, of the line passing through points (-4,-3) and (0,-2)
How to do this I’m lost
Please solve both and tell me how!
what is the solution to 11/(2x+5) = 12/2x
if 20 students ride on your bus and two fifth of them pack there lunches how many of them didnt pack there lunch
what is the length of leg s of the triangle below?
A circular table has a diameter of 4ft.what is its approximate area?(use pi=3)