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Home » 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 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.
CBSE | Class 10 | Coordinate Geometry | Maths | NCERT
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.

Solution:

The coordinates of points A, B, C, and D are (3, 4), (6, 7), (9, 4) and (6, 1), respectively, as shown in the figure. Using the distance formula, we can calculate the distance between two places.

AB=\sqrt{{{\left( 6-3 \right)}^{2}}+{{\left( 7-4 \right)}^{2}}}=\sqrt{9+9}=3\sqrt{2}

BC=\sqrt{{{\left( 9-6 \right)}^{2}}+{{\left( 4-7 \right)}^{2}}}=\sqrt{9+9}=3\sqrt{2}

CD=\sqrt{{{\left( 6-9 \right)}^{2}}+{{\left( 1-4 \right)}^{2}}}=\sqrt{9+9}=3\sqrt{2}

DA=\sqrt{{{\left( 6-3 \right)}^{2}}+{{\left( 1-4 \right)}^{2}}}=\sqrt{9+9}=3\sqrt{2}

AB = BC = CD = DA = 3\sqrt{2} Each side is of the same length. As a result, ABCD is a square, indicating that Champa was correct.

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