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Coordinate Geometry

Short Answer Type

111. Find the distance between the following pairs of points :
(2, 3), (4, 1)

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112. Find the distance between the following pairs of points :
(– 5, 7), (– 1, 3)

1641 Views

113. Find the distance between the following pairs of points :
(a, b), (– a, – b)

988 Views

114.

Find the distance between the points (0, 0) and (36, 15). Can you now find the distance between the two towns A and B discussed in Section 7.2.

843 Views

115.

Determine if the points (1, 5), (2, 3) and (– 2, – 11) are collinear

1618 Views

116.

Check whether (5, – 2), (6, 4) and (7, – 2) are the vertices of an isosceles triangle.

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117.

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.

Fig. 7.8

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118.

Name the type of quadrilateral formed, if any, by the following points, and give reasons for your answer:
(-1, -2), (1, 0), (-1, 2), (-3, 0)

140 Views

119.

Name the type of quadrilateral formed, if any, by the following points, and give reasons for your answer:
(–3, 5), (3, 1), (0, 3), (–1, – 4)

167 Views

120.
Name the type of quadrilateral formed, if any, by the following points, and give reasons for your answer:
(4, 5), (7, 6), (4, 3), (1, 2)

Let the given points be A(4, 5), B(7, 6), C(4, 3) and D(1, 2).

Then comma space space AB space equals space square root of open parentheses 7 minus 4 close parentheses squared plus left parenthesis 6 minus 5 right parenthesis squared end root rightwards double arrow space space space space space space AB space equals square root of open parentheses 3 close parentheses squared plus left parenthesis 1 right parenthesis squared end root equals square root of 9 plus 1 end root equals square root of 10 space space space space space space space space space space BC space equals square root of open parentheses 4 minus 7 close parentheses squared plus left parenthesis 3 minus 6 right parenthesis squared end root rightwards double arrow space space space space space space BC space equals space square root of open parentheses negative 3 close parentheses squared plus left parenthesis negative 3 right parenthesis squared end root rightwards double arrow space space space space space space BC space equals space square root of 9 plus 9 end root equals square root of 18 space space space space space space space space space CD space equals space square root of left parenthesis 1 minus 4 right parenthesis squared plus left parenthesis 2 minus 3 right parenthesis squared end root rightwards double arrow space space space space space CD space space equals space square root of left parenthesis negative 3 right parenthesis squared plus left parenthesis negative 1 right parenthesis squared end root rightwards double arrow space space space space space space CD space equals space square root of 9 plus 1 end root equals square root of 10 and space space space DA space equals square root of left parenthesis 4 minus 1 right parenthesis squared plus left parenthesis 5 minus 2 right parenthesis squared end root rightwards double arrow space space space space DA space equals space square root of left parenthesis 3 right parenthesis squared plus left parenthesis 3 right parenthesis squared end root rightwards double arrow space space space space DA space equals space square root of 9 plus 9 end root equals square root of 18 space space space

Here, we have

AB space equals space CD space equals space square root of 10 And comma space space space space BC space equals space DA space equals space square root of 18

rightwards double arrow

Opposite sides of quardrilateral are equal.

Also comma space space space space AC space equals space square root of left parenthesis 4 minus 4 right parenthesis squared plus left parenthesis 3 minus 5 right parenthesis squared end root rightwards double arrow space space space space space space space AC space equals space square root of 0 plus left parenthesis negative 2 right parenthesis squared end root rightwards double arrow space space space space space space space AC space equals space square root of 0 plus 4 end root equals square root of 4 equals 2 and space space space BD space equals space square root of open parentheses 1 minus 7 close parentheses squared plus left parenthesis 2 minus 6 right parenthesis squared end root rightwards double arrow space space space space BD space space equals space square root of left parenthesis negative 6 right parenthesis squared plus left parenthesis negative 4 right parenthesis squared end root rightwards double arrow space space space space BD space space equals space space square root of 36 plus 16 end root equals square root of 52

Here, sides AB = DC and BC = AD but diagonals are not equal. Therefore, quadrilateral formed by given points is a parallelogram.

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Previous Year Papers

Test Series

Test Yourself

Short Answer Type

120. Name the type of quadrilateral formed, if any, by the following points, and give reasons for your answer:(4, 5), (7, 6), (4, 3), (1, 2)

120.
Name the type of quadrilateral formed, if any, by the following points, and give reasons for your answer:
(4, 5), (7, 6), (4, 3), (1, 2)