SATHEE: Straight Line and Pair of Straight Lines 1 Question 39

Straight Line and Pair of Straight Lines 1 Question 39

39. The point $(4, 1)$ undergoes the following three transformations successively

I. Reflection about the line $y = x$ .

II. Transformation through a distance 2 units along the positive direction of $X$ -axis.

III. Rotation through an angle $\frac{π}{4}$ about the origin in the counter clockwise direction.

Then, the final position of the point is given by the coordinates

(1980, 1M)

(a) $\frac{1}{\sqrt{2}}, \frac{7}{\sqrt{2}}$

(b) $(- \sqrt{2}, 7 \sqrt{2)}$

(d) $(\sqrt{2,} 7 \sqrt{2)}$

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Solution:

Let $B, C, D$ be the position of the point $A (4, 1)$ after the three operations I, II and III, respectively. Then, $B$ is $(1, 4), C (1 + 2, 4)$ i.e. $(3, 4)$ . The point $D$ is obtained from $C$ by rotating the coordinate axes through an angle $π / 4$ in anti-clockwise direction.

Therefore, the coordinates of $D$ are given by

$\begin{aligned} X & = 3 \cos \frac{π}{4} - 4 \sin \frac{π}{4} = - \frac{1}{\sqrt{2}} \\ and Y & = 3 \sin \frac{π}{4} + 4 \cos \frac{π}{4} = \frac{7}{\sqrt{2}} \end{aligned}$

$∴$ Coordinates of $D$ are $- \frac{1}{\sqrt{2}}, \frac{7}{\sqrt{2}}$ .

Straight Line and Pair of Straight Lines 1 Question 39

39. The point $(4, 1)$ undergoes the following three transformations successively

Solution:

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Straight Line and Pair of Straight Lines 1 Question 39

39. The point (4,1) undergoes the following three transformations successively

Solution:

Engineering Preparation

Medical Preparation

NCERT Books & Solutions

Important Resources

Other Resources

Syllabus

Test Platform

Sample Mock Test

Mentorship

NCERT Exercise Video Solution

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39. The point $(4, 1)$ undergoes the following three transformations successively