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Introduction To Trigonometry

Question
CBSEENMA10006991
Wired Faculty App

Find the coordinates of the points of trisection of the line segment joining (4, –1) and (–2, –3).

Solution

Let P and Q be the point of trisection of AB. Then,

AP = PQ = QB = 1
Case I. Here P divides AB in the ratio 1 : 2.
So, we have
x1 = 4, y1 = -1
x2 = -2, y2 = -3
and    m1 = 1, m2 = 2
∴ The coordinates of P are given by

Case II. Here, Q divides AB in the ratio 2 : 1. So, we have
x1 = 4, y1 = -1
x2 = 2, y2 = -3
and    m1 = 2, m2 = 1
∴ The coordinates of Q are given by

Some More Questions From Introduction to Trigonometry Chapter

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

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)

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