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Show that the points (1,7),(4,2),(-1,-1),(-4,4) are …

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Show that the points (1,7),(4,2),(-1,-1),(-4,4) are the vertices of a square?

Posted by Subhra Bera 5 years, 6 months ago

CBSE > Class 10 > Mathematics

1 answers

Gaurav Seth 5 years, 6 months ago

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.

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