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