Q20 of 184 Page 10

Prove that the points (4, 3), (6, 4), (5, 6) and (- 4, 4) are the vertices of a square.

Given points are A(4, 3), B(6, 4), C(5, 6) and D(- 4, 4).



We need to prove that these are the vertices of a square.


We know that in the lengths of all sides are equal and the lengths of the diagonals are equal.


Let us find the lengths of the sides.


We know that the distance between the points (x1, y1) and (x2, y2) is .


Now,


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We got AB = BC≠CD≠DA,


∴ The points doesn’t form a square.


More from this chapter

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19

The centre of the circle is (2x - 1, 3x + 1) and radius is 10 units. Find the value of x if the circle passes through the point (- 3, - 1).

 20

Prove that the points (4, 3), (6, 4), (5, 6) and (3, 5) are the vertices of a square.

 21

Prove that the points (3, 2), (6, 3), (7, 6), (4, 5) are the vertices of a parallelogram. Is it a rectangle?

 22

Prove that the points (6, 8), (3, 7), (- 2, - 2), (1, - 1) are the vertices of a parallelogram.