Math, asked by AdvikaRai809, 9 months ago

Show that the following points form a right triangle calculate the area. The points are (-4,-1),(-2,-4), (4,0).

Answers

Answered by VJTHUNDER
0

Step-by-step explanation:

Yes it is a rectangle.

Step-by-step explanation:

Given : Points (-4,-1) , (-2,-4) , (4,0) , (2,3)

To show : The points are the vertices points of a rectangle.

Solution :

We know, opposite sides are equal form a rectangle.

We find the distance between two points and check any two sides are equal or not.

Let A=(-4,-1), B=(-2,-4), C=(4,0), D=(2,3)

Distance between two points is D=\sqrt{(x-x_1)^2+(y-y_1)^2}D=

(x−x

1

)

2

+(y−y

1

)

2

Length AB , BC, CD, AD is

\begin{lgathered}AB=\sqrt{(-4+2)^2+(-1+4)^2}\\AB=\sqrt{4+9}\\AB=\sqrt{13}\end{lgathered}

AB=

(−4+2)

2

+(−1+4)

2

AB=

4+9

AB=

13

\begin{lgathered}BC=\sqrt{(4+2)^2+(0-4)^2}\\BC=\sqrt{36+16}\\BC=\sqrt{52}\end{lgathered}

BC=

(4+2)

2

+(0−4)

2

BC=

36+16

BC=

52

\begin{lgathered}CD=\sqrt{(2-4)^2+(3-0)^2}\\CD=\sqrt{4+9}\\CD=\sqrt{13}\end{lgathered}

CD=

(2−4)

2

+(3−0)

2

CD=

4+9

CD=

13

\begin{lgathered}AD=\sqrt{(2+4)^2+(3+1)^2}\\AD=\sqrt{36+16}\\AD=\sqrt{52}\end{lgathered}

AD=

(2+4)

2

+(3+1)

2

AD=

36+16

AD=

52

Since, AB=CD , BC=AD

which shows it form a rectangle.

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