Question

Show that the points (1, 7), (4, 2), (–1, –1) and (– 4, 4) are the vertices of a square.

Answer 1

Given points are (1,7),(4,2),(-1,-1),(-4,4)
Let the points are A,B,C,D.
Distance formula = √(x₂-x₁)²+(y₂-y₁)²
                    AB = √(4-1)²+(2-7)²
                          = √9+25
                          = √34
                     BC = √(-1-4)²+(-1-2)²
                           = √25+9
                           =  √34
                      CD = √(-4-(-1))²+(4-(-1))²
                            = √9+25
                            =  √34
                       DA = √(1-(-4))²+(7-4)²
                             = √25+9
                             = √34
We know that the all sides of the square are equal.
Here by the distance formula, we got the for sides equal .
So,from this we can say that these points are the vertices of a square.

Answer 2

Answer:

Step-by-step explanation:

Given points are (1,7),(4,2),(-1,-1),(-4,4)

Let the points are A,B,C,D.

Distance formula = √(x₂-x₁)²+(y₂-y₁)²

                   AB = √(4-1)²+(2-7)²

                         = √9+25

                         = √34

                    BC = √(-1-4)²+(-1-2)²

                          = √25+9

                          =  √34

                     CD = √(-4-(-1))²+(4-(-1))²

                           = √9+25

                           =  √34

                      DA = √(1-(-4))²+(7-4)²

                            = √25+9

                            = √34

We know that the all sides of the square are equal.

Here by the distance formula, we got the for sides equal .

So,from this we can say that these points are the vertices of a square.