Question

show that the point (-4,-1) ,(-2,-4), (4,0)&(2,3) are the vertices points of a rectangle​

Answer 1

A(−4,−1), B(−2,4), C(4,0) and D(2,3) be the given points

we know that, distance formula = √(x_2-x_1)²+(y_2-y_1)²

Now, AD= √(2+4)²+(3+1)²= √52

BC= √(4+2)²+(0+4)²= √52

AB= √(−2+4)²+(−4+1)² = √4+9 = √13

CD= √(2−4)² +(3−0)² = √13

⇒ AD=BC and AB=CD

Now, AC= √(4+4)² +(0+1)² = √65

BD= √(2+2)² +(3+4)² = √65

⇒ AC=BD

Hence, ABCD is a rectangle

⇒ Therefore, the point (-4,-1) ,(-2,-4), (4,0)&(2,3) are the vertices points of a rectangle.

Hope this will help you...