1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Degger [83]
3 years ago
6

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

egative 1, negative 2). At which points could the vertex of the right angle in the triangle be located? Check all that apply. (–1, 1) (4, –2) (1, 1) (2, –2) (4, –1) (–1, 4)

Mathematics
2 answers:
lina2011 [118]3 years ago
8 0

Answer:

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

Step-by-step explanation:

GarryVolchara [31]3 years ago
7 0

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)

You might be interested in
My bike travels 7 feet in 1/3 seconds. How many feet can I travel in 5 seconds?
slavikrds [6]
21 feet hope this helps
4 0
3 years ago
If JK = 7, KH = 21, and JL = 6, find LI, x and TV.
Natali [406]

As per given:

\begin{gathered} \frac{JK}{KH}=\frac{JL}{LI} \\ \frac{7}{21}=\frac{6}{LI} \\ LI=\frac{21\times6}{7} \\ LI=3\times6 \\ LI=18 \end{gathered}

6 0
1 year ago
An aquarium tank can hold 6000 liters of water. There are two pipes that can be used to fill the tank. The first pipe alone can
Usimov [2.4K]
The answer is 24 minutes
7 0
3 years ago
Which is the graph of y= -x + 2?<br><br> A<br> B<br> C<br> D
Vladimir [108]

Answer:

hdhdjdkjfhfhdodjdbhddkdjdbhdjdodjdjjdnfnn

6 0
3 years ago
Read 2 more answers
Helppp me plz Srry again
Kay [80]

Step-by-step explanation:

<em>I</em><em> </em><em>a</em><em>m</em><em> </em><em>r</em><em>e</em><em>a</em><em>l</em><em>l</em><em>y</em><em> </em><em>v</em><em>e</em><em>r</em><em>y</em><em> </em><em>s</em><em>o</em><em>r</em><em>r</em><em>y</em><em> </em><em>a</em><em>b</em><em>o</em><em>u</em><em>t</em><em> </em><em>t</em><em>h</em><em>i</em><em>s</em><em> </em><em>b</em><em>e</em><em>c</em><em>a</em><em>u</em><em>s</em><em>e</em><em> </em><em>I</em><em> </em><em>c</em><em>a</em><em>n</em><em>'</em><em>t</em><em> </em><em>a</em><em>n</em><em>s</em><em>w</em><em>e</em><em>r</em><em> </em><em>o</em><em>f</em><em> </em><em>t</em><em>h</em><em>i</em><em>s</em><em> </em><em>q</em><em>u</em><em>e</em><em>s</em><em>t</em><em>i</em><em>o</em><em>n</em><em> </em><em>b</em><em>e</em><em>c</em><em>a</em><em>u</em><em>s</em><em>e</em><em> </em><em>I</em><em> </em><em>c</em><em>a</em><em>n</em><em>'</em><em>t</em><em> </em><em>u</em><em>n</em><em>d</em><em>e</em><em>r</em><em>s</em><em>t</em><em>a</em><em>n</em><em>d</em><em> </em><em>I</em><em> </em><em>a</em><em>m</em><em> </em><em>s</em><em>o</em><em>o</em><em>o</em><em>o</em><em>o</em><em> </em><em>s</em><em>o</em><em>r</em><em>r</em><em>y</em>

4 0
3 years ago
Other questions:
  • What are the solutions of the equation? 0=x^2-2x-24
    7·1 answer
  • Find value of x in circle O
    10·1 answer
  • If the area of a trapezoid is 57cm2 and one of the bases is 11cm what is the length of the other base?
    6·1 answer
  • You take a train away from Bangkok at 1:50 a.m. on Wednesday. You ride the train for 16 hours and 40 minutes, at which point you
    12·1 answer
  • The four highest scores on the floor exercise at a gymnastics meet were 9.675, 9.25, 9.325, and 9.5. List the scores from least
    5·2 answers
  • The measures of the angles of a triangle are shown in the figure below. Solve for x.
    14·2 answers
  • Which of the following is NOT a function?
    10·1 answer
  • Solve for x in a triangle. Round your answer to the nearest hundredth
    12·2 answers
  • Suppose City A is 50.2 km east of City B. City C is 124.4 km east of City B. How far apart are City A and City​ C?
    14·1 answer
  • There are 738 students going on a school field trip. Each bus can carry 33 students. How many buses should the school reserve? b
    5·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!