Question

The points(1,7), (4,2), (-1,1) and (-4,4) are the vertices of a

parallelogram

rhombus

rectangle

square
​

Answer 1

Answer:

parallelogram is the correct answer

Answer 2

Step-by-step explanation:

Let A(1,7),B(4,2),C(−1,−1) and D(4,4)

Distance between two points (x

1

,y

1

) and (x

2

,y

2

) can be calculated using the formula

(x

2

−x

1

)

2

+(y

2

−y

1

)

2

Distance between the points A(1,7) and B (4,2)=

(4−1)

2

+(2−7)

2

=

9+25

=

34

Distance between the points B(4,2) and C (−1,−1)=

(−1−4)

2

+(−1−2)

2

=

25+9

=

34

Distance between the points C(−1,−1) and D (−4,4)=

(−4+1)

2

+(4+1)

2

=

9+25

=

34

Distance between the points A(1,7) and D (−4,4)=

(−4−1)

2

+(4−7)

2

=

25+9

=

34

Since, length of the sides between all vertices are equal, they are the vertices of a square.