From (1,4) you travel 5 √2 units by making 135° angle with positive x-axis (anticlockwise) and then 4 units by making 120° angle with positive x-axis (clockwise) to reach Q. Find co-ordinates of point Q.

Question

From (1,4) you travel 5 √2 units by making 135° angle with positive x-axis (anticlockwise) and then 4 units by making 120° angle with positive x-axis (clockwise) to reach Q. Find co-ordinates of point Q. (A) (+6,9-2 √3) (B) (-6,9-2 √3) (C) (-6,9+2 √3) (D) (+6,9+2 √3)

Tardigrade Admin · Accepted Answer

<img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/mathematics/2f2e4211f0d61a64a850d5b9f4b1ff2d-.png" /> For point P (x-1/ cos 135°)=(y-4/ sin 135°)=5 √2 ⇒ x=-4, y=9 For point Q (x+4/ cos (-120°))=(y-9/ sin (-120°))=4 ⇒ x=-6, y=9-2 √3 ∴ Q(-6,9-2 √3).

Q. From $(1, 4)$ you travel $52$ units by making $13 5^{\circ}$ angle with positive $x$ -axis (anticlockwise) and then $4$ units by making $12 0^{\circ}$ angle with positive $x$ -axis (clockwise) to reach $Q$ . Find co-ordinates of point $Q$ .

$(+ 6, 9 - 23)$

$(- 6, 9 - 23)$

$(- 6, 9 + 23)$

$(+ 6, 9 + 23)$

For point $P \frac{x - 1}{c o s 13 5 ^{\circ}} = \frac{y - 4}{s i n 13 5 ^{\circ}} = 52$
$\Rightarrow x = - 4, y = 9$
For point $Q$
$\frac{x + 4}{c o s ( - 12 0 ^{\circ} )} = \frac{y - 9}{s i n ( - 12 0 ^{\circ} )} = 4$
$\Rightarrow x = - 6, y = 9 - 23$
$∴ Q (- 6, 9 - 23)$ .

Q. From (1,4) you travel 52​ units by making 135∘ angle with positive x-axis (anticlockwise) and then 4 units by making 120∘ angle with positive x-axis (clockwise) to reach Q. Find co-ordinates of point Q.

(+6,9−23​)

(−6,9−23​)

(−6,9+23​)

(+6,9+23​)