Anybody know the answer to these

The hypotenuse of a right triangle has endpoints A(4, 1) and B(–1, –2). On a coordinate plane, line A B has points (4, 1) and (n

GarryVolchara [31]

Answer:

$(-1,1),(4,-2)$

Step-by-step explanation:

Given: The hypotenuse of a right triangle has endpoints A(4, 1) and B(–1, –2).

To find: coordinates of vertex of the right angle

Solution:

Let C be point $(x,y)$

Distance between points $(x_1,y_1),(x_2,y_2)$ is given by $\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

$AC=\sqrt{(x-4)^2+(y-1)^2}\\BC=\sqrt{(x+1)^2+(y+2)^2}\\AB=\sqrt{(4+1)^2+(1+2)^2}=\sqrt{25+9}=\sqrt{34}$

ΔABC is a right angled triangle, suing Pythagoras theorem (square of hypotenuse is equal to sum of squares of base and perpendicular)

$34=\left [ (x-4)^2+(y-1)^2 \right ]+\left [ (x+1)^2+(y+2)^2 \right ]$

Put $(x,y)=(-1,1)$

$34=\left [ (-1-4)^2+(1-1)^2 \right ]+\left [ (-1+1)^2+(1+2)^2 \right ]\\34=25+9\\34=34$

which is true. So, $(-1,1)$ can be a vertex

Put $(x,y)=(4,-2)$

$34=\left [ (4-4)^2+(-2-1)^2 \right ]+\left [ (4+1)^2+(-2+2)^2 \right ]\\34=9+25\\34=34$

which is true. So, $(4,-2)$ can be a vertex

Put $(x,y)=(1,1)$

$34=\left [ (1-4)^2+(1-1)^2 \right ]+\left [ (1+1)^2+(1+2)^2 \right ]\\34=9+4+9\\34=22$

which is not true. So, $(1,1)$ cannot be a vertex

Put $(x,y)=(2,-2)$

$34=\left [ (2-4)^2+(-2-1)^2 \right ]+\left [ (2+1)^2+(-2+2)^2 \right ]\\34=4+9+9\\34=22$

which is not true. So, $(2,-2)$ cannot be a vertex

Put $(x,y)=(4,-1)$

$34=\left [ (4-4)^2+(-1-1)^2 \right ]+\left [ (4+1)^2+(-1+2)^2 \right ]\\34=4+25+1\\34=30$

which is not true. So, $(4,-1)$ cannot be a vertex

Put $(x,y)=(-1,4)$

$34=\left [ (-1-4)^2+(4-1)^2 \right ]+\left [ (-1+1)^2+(4+2)^2 \right ]\\34=25+9+36\\34=70$

which is not true. So, $(-1,4)$ cannot be a vertex

So, possible points for the vertex are $(-1,1),(4,-2)$

7 0

2 years ago

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The point (- 3, 2) is on the line given by which equation below?

My name is Ann [436]

Answer:

what equation below? :/

Step-by-step explanation:

5 0

3 years ago

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Xyz-qrs and the scale factor from xyz to qrs is 2/5. what is the length of side rs?

raketka [301]

Answer:

RS = 10

Step-by-step explanation:

We are told that to get ∆QRS, the scale factor of ⅖ was used. To get side RS, we would multiply the side length of the side that corresponds to RS.

YZ corresponds to RS.

YZ = 25

Thus,

RS = 25*⅖

RS = 10

3 0

2 years ago

Explain how to use patterns or sequences to determine the last digit of the number 7N, where N is the four-digit year of your bi

maria [59]

Ahh this is a good hard question, hopefully someone comes along and helps you out with it. Goodluck my friend!

7 0

2 years ago

Which of the following describes an effective strategy for protecting yourself against identity theft? A. Shredding all importan

givi [52]

The <u>correct answer</u> is:

C) Avoid using unsecured wireless networks.

Explanation:

Using an unsecured wireless network puts your information at risk. If you use an open network, that means that absolutely anyone within range can access the same network you are on, which opens you up to potential scammers, phishers, etc.

On the other hand, using a secured network decreases the number of people on the same network as you, since they will have to have the same password to access the network. This helps prevent your information from falling into the wrong hands.

5 0

3 years ago

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