Question

show that the points (- 4 - 1), (- 2, - 4) (- 4, 0), and 2, 3 at the vertex of a rectangle​

Answer 1

Answer:

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}

Length AB , BC, CD, AD is

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

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

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

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

Since, AB=CD , BC=AD

which shows it form a rectangle.

Answer 2

Answer:

prove that the points (-7,-3),(5,10