+91-8076753736[email protected]
logo
logo
-->

Introduction To Trigonometry

Question
CBSEENMA10006985
Wired Faculty App

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) 

Solution
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.

Some More Questions From Introduction to Trigonometry Chapter

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

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)

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)

Find the values of y for which the distance between the points P(2, – 3) and Q(10, y) is 10 units.

Find a relation between x and y such that the point (x, y) is equidistant from the point (3, 6) and (-3, 4).

Mock Test Series

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation