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mars1129 [50]
3 years ago
14

What are the coordinates of the image of point (−1, 5) after a counterclockwise rotation of 90º about the origin?

Mathematics
2 answers:
Andreas93 [3]3 years ago
8 0
-5,0 would be the correct answer
gladu [14]3 years ago
7 0

Answer:

(-5,-1)

Step-by-step explanation:

We have been given the coordinates of a point and we are asked to find the coordinates of he point after a counterclockwise rotation of 90º about the origin.  

We know that after rotating a point 90 degree counter-clockwise about the origin, the x and y-coordinates changes places with each other and x-coordinate of new point becomes the negative of y-coordinate.

(x,y)\rightarrow (-y,x)

Applying the rotation rule the coordinates of new point would be:

(-1,5)\rightarrow (-5,-1)

Therefore, the required coordinates of the given point after a counterclockwise rotation of 90º about the origin would be (-5,-1).

You might be interested in
Which point-slope equation represents a line that passes through (3,-2) with a slope of -4/5?
Viefleur [7K]

Answer:

y + 2 = -4/5 (x - 3)

Step-by-step explanation:

y - y1 = m (x - x1). Put in your points for y1 and x1, and always remember to flip your signs.

unfortunately, I don't know why that isn't one of your answers, so sticking with the positive 2 I would choose y+2=- (- 3) if I were you. Looks like the -4/5 disappeared somehow?

Hope this helps

8 0
2 years ago
In a survey of 3400 people asked about their ice cream preference, 1600 enjoyed chocolate, 1250 enjoyedvanilla, 1700 enjoyed min
velikii [3]

Answer:

Step-by-step explanation:

To understand the situations we must do a Venn diagram:

The total of people asked is 3400. Then,

a) For People who enjoyed vanilla but not chocolate or mint, seeing the diagram of Venn, we can deduce the equations:

undefined

b) For people who did not enjoy chocolate, vanilla or mint:

undefined

4 0
1 year ago
PLEASE PLEASE PLEASE HELP ME WITH ALGEBRA 1 PLEASE!?!?!?!?!!!?!?!?!?!?! I WILL GIVE LOTS OF POINTS AND BRAINLEST
Damm [24]

<span>1.1 What are the different ways you can solve a system of linear equations in two variables? 

</span><span>A linear equation can be written in many ways, so the way we can use to solve a system of linear equations depends on the form the system is written. There are several methods to do this, the more common are: Method of Equalization, Substitution Method, Elimination Method. 

<span>1.2. Method of Equalization

</span>a. Write the two equations in the style [variable = other terms] either variable x or y.<span>
</span>b. Equalize the two equations 
c. Solve for the other variable and then for the first variable.

</span>

<span> 1.3. Substitution Method

a. Write one of the equations (the one that looks the simplest equation) in the style [variable = other terms] either variable x or y.
b. Substitute that variable in the other equation and solve using the usual algebra methods.
c. Solve the other equation for the other variable.<span>

1.4. Elimination Method

Eliminate</span> means to remove, so this method works by removing variables until there is just one left. The process is:
<span>
</span>a. Multiply an equation by a constant "a" such that there is a term in one equation like [a*variable] and there is a term in the other equation like [-a*variable]
b. Add (or subtract) an equation on to another equation so the aim is to eliminate the term (a*variable)
c. Solving for one variable and the for the other.
</span>

2.1 Benefits of Method of Equalization<span>
</span>


It's useful for equations that are in the form [variable = other terms] (both equations). In this way, it is fast to solve the system of linear equation by using this method. The limitations come up as neither of the equations are written in that way, so it would be necessary to rewrite the two equations to achieve our goal


2.2. Benefits and limitations of Substitution Method


This method is useful for equations that at least one of them is in the form [variable = other terms]. So unlike the previous method, you only need one equation to be expressed in this way. Hence, it is fast to solve the system of linear equation by using this method. The limitations are the same that happens with the previous method, if neither of the equations is written in that way, we would need to rewrite one equation to achieve our goal.


2.3. Benefits and limitations of Elimination Method


It's useful for equations in which the term [a*variable] appears in one equation and the term [-a*variable] appears in the other one, so adding (or subtracting). 


3.1. What are the different types of solutions


When the number of equations is the same as the number of variables there is likely to be a solution. Not guaranteed, but likely.

One solution: It's also called a consistent system. It happens as each equation gives new information, also called Linear Independence.

An infinite number of solutions: It's also called a consistent system, but happens when the two equations are really the same, also called Linear Dependence.

No solutions: It happens when they are actually parallel lines. 


3.2. Graph of one solution system


See figure 1, so there must be two straight lines with different slopes.


3.3. Graph of infinite number of solutions system


See figure 2. So there must be two straight lines that are really the same.


3.4. Graph of no solution system


See figure 3. So there must be two straight lines that are parallel.


4. Explain how using systems of equations might help you find a better deal on renting a car?


Q. A rental car agency charges $30 per day plus 10 cents per mile to rent a certain car. Another agency charges $20 per day plus 15 cents per mile to rent the same car. If the car is rented for one day in how many miles will the charge from both agencies be equal?

A. Recall: 10 cents = 0.1$, 15 cents = 0.15$

If you rent a car from the first car agency your cost for the rental will be:

(1) 30D+0.1M

<span>If you rent a car from the second car agency the total amount of money to pay is:

(2) 20D+0.15M</span>

Given that the problem says you want to rent the car just for one day, then D = 1, therefore:

First agency: 30(1)+0.1M=&#10;\boxed{30+0.1M}

Second agency: 20(1)+0.15M=&#10;\boxed{20+0.15M}

<span>At some number of miles driven the two costs will be the same:

30+0.1M=20+0.15M

Solving for M:

10=0.05M
M=200mi

There is a representation of this problem in figure 4. Up until you drive 200 miles you would save money by going with the second company.</span>

<span>

5. Describe different situations in the real world that could be modeled and solved by a system of equations in two variables </span>

<span>
</span>

For example, if you want to choose between two phone plans. The plan with the first company costs a certain price per month with calls costing an additional charge in cents per minute. The second company offers another plan at a certain price per month with calls costing an additional charge in cents per minute. So depending on the minutes used you should one or another plan.


3 0
3 years ago
Please help me asap!!!
blondinia [14]

Answer:

the answer is 120.6                     (:

Step-by-step explanation:

3 0
3 years ago
If the length of line segment AB is 9 inches, the total number of point 4 inches from Point A and 6 inches from Point B is
brilliants [131]

9514 1404 393

Answer:

 B.  Two

Step-by-step explanation:

There are two points that are 4 inches from A and 6 inches from B.

__

<em>Additional comment</em>

They are at the intersection points of circle A with radius 4 inches and circle B with radius 6 inches.

4 0
2 years ago
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