In a classroom, 4 friends are seated at the points A, B, C and D as shown in Fig. 7.8. Champa and Chameli walk into the class and after observing for a few minutes Champa asks Chameli, “Don’t you think ABCD is a square?” Chameli disagrees. Using distance formula, find which of them is correct.

In a classroom, 4 friends are seated at the points, A, B, C and D as shown  in the following figure. - Sarthaks eConnect | Largest Online Education  Community

Asked by Abhisek | 1 year ago |  103

1 Answer

Solution :-

From figure, the coordinates of points A, B, C and D are (3, 4), (6, 7), (9, 4) and (6,1).

Find distance between points using distance formula, we get

AB=BC=CD=DA \( 3\sqrt{2}\) and diagonals AC=BD=6

All sides are of equal length. Therefore, ABCD is a square and hence, Champa was correct.

Answered by Pragya Singh | 1 year ago

Related Questions

In the determine whether the given quadratic equations have real roots and if so, And the roots 3x2 – 2x + 2 = 0

Class 10 Maths Coordinate Geometry View Answer

Find the point on x-axis which is equidistant from the points (-2, 5) and (2, -3).

Class 10 Maths Coordinate Geometry View Answer

Answer the following questions:-

(i) Show that the points A (5, 6), B (1, 5), C (2, 1) and D (6, 2) are the vertices of a square. 

(ii) Prove that the points A (2, 3), B (-2, 2), C (-1, -2) and D (3, -1) are the vertices of a square ABCD.

(iii) Name the type of triangle PQR formed by the point \( P(\sqrt{2} , \sqrt{2}), Q(- \sqrt{2}, – \sqrt{2)} and\; R (-\sqrt{6} , \sqrt{6} )\)

Class 10 Maths Coordinate Geometry View Answer

Find a point on the x-axis which is equidistant from the points (7, 6) and (-3, 4).

Class 10 Maths Coordinate Geometry View Answer

Find the coordinates of the circumcentre of the triangle whose vertices are (3, 0), (-1, -6) and (4, -1). Also, find its circumradius.
 

Class 10 Maths Coordinate Geometry View Answer