RD Sharma Solutions for Class 11 Maths Exercise 22.1 Chapter 22 - Brief review of Cartesian System of Rectangular Coordinates

Here, in this exercise, we shall discuss concepts related to the cartesian coordinates of a point, the distance between two points and finding the area of a triangle. Students who aim to secure good marks in the board exams are advised to refer to RD Sharma Class 11 Maths Solutions. The solutions are formulated by our expert tutors in a step-by-step manner to help students understand the concepts clearly. Students are advised to practise regularly on a daily basis to come out with flying colours in their board examination. The PDF of RD Sharma Class 11 Maths Solutions is provided in the link given below, which can be downloaded easily and can be used for future reference as well.

RD Sharma Solutions for Class 11 Maths Exercise 22.1 Chapter 22 – Brief Review of Cartesian System of Rectangular Coordinates

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Access answers to RD Sharma Solutions for Class 11 Maths Exercise 22.1 Chapter 22 – Brief review of Cartesian System of Rectangular Coordinates

1. If the line segment joining the points P(x₁, y₁) and Q(x₂, y₂) subtends an angle α at the origin O, prove that: OP. OQ cos α = x₁ x₂ + y₁ y₂.

Solution:

Given,

Two points, P and Q, subtend an angle α at the origin, as shown in the figure:

From figure, we can see that points O, P and Q form a triangle.

Clearly, in ΔOPQ we have:

2. The vertices of a triangle ABC are A(0, 0), B (2, -1) and C (9, 0). Find cos B.

Solution:

Given:

The coordinates of the triangle.

From the figure,

By using the cosine formula,

In ΔABC, we have:

3. Four points A (6, 3), B (-3, 5), C (4, -2) and D (x, 3x) are given in such a way that , find x.

Solution:

24.5 = 28x – 14

28x = 38.5

x = 38.5/28

= 1.375

4. The points A (2, 0), B (9, 1), C (11, 6) and D (4, 4) are the vertices of a quadrilateral ABCD. Determine whether ABCD is a rhombus or not.

Solution:

Given:

The coordinates of 4 points that form a quadrilateral are shown in the below figure

Now by using the distance formula, we have:

It is clear that AB ≠ BC [quad ABCD does not have all 4 sides equal.]

∴ ABCD is not a Rhombus