If the vertices of a parallelogram pqrs taken in order

Views: 5,584 12.30 MATIEINTIC - x ) 8. A vertically straight tree, 15 m high, is broken by the wind ir such a way that its top iust touches the ground and makes an angle of 6 0 ∘ with the ground. At what heghifrop ius the bertical flag-stafr] 9. A vertical tower stands on a horizontal plane and is surmounted by a verticat flestion of top of the flag-staff are respectively 3 0 ∘ and 6 0 ∘. Find the height of the tower 10. A person observed the angle of elevation of the top of a tower as 3 0 ∘. He walked 50 m towards the foot of the fower along level ground and found the angle of elevation of the top of the tower as 6 0 ∘. Find the height of the tower. 11. The shadow of a tower, when the angle of elevation of the sun is 4 5 ∘, is found to be 10 m longer than when it was 6 0 ∘. Find the height of the tower. 12. A parachutist is descending ver tically and makes angles of elevation of 4 5 ∘ and 6 0 ∘ at two observing points 100 m apart from each other on the left side of himself. Find the maximum height from which he falls and the distance of the point where he falls on the ground from the just observation point. 13. On the same side of a tower, two objects are located. When observed from the top of the tower, their angles of depression are 4 5 ∘ and 6 0 ∘. If the height of the tower is 150 m, find the distance between the objects. Views: 5,554 β α 2 ​ and α β 2 ​ . Long Answer Type Questions (5 marks each) 13. If α and β are the zeroes of the quadratic polynomial f ( x ) = k x...

Views: 5,600 5.31 Fig. 5.32 14. A B and C D are respectively arcs of two concentric circles of radii 21 cm and am and centre O (see Fig. 5.32). If ∠ A OB = 3 0 ∘, find the area of the shaded region. 15. In Fig. 5.33, ABC is a quadrant of a circle of radius 14 cm and a semicircle is drawn with BC as diameter. Find the area of the shaded region.

It is given in the question that, The vertices of a parallelogram PQRS taken in order are P(3,4), Q(-2,3) and R(-3,-2) Let, the fourth vertices is S (x , y). The parallelogram's PQRS's vertices, listed in order. Because of this, a parallelogram's diagonals are split in half. We know that the diagonals of a parallelogram bisects with each other. ∴ Coordinates of the PR's midpoint = coordinates for QS's midpoint \begin1=23+y​2=3+yy=−1​ the coordinates of its fourth vertex S are (2,-1).

So. option (d) is correct. Q 2 5. If the vertices of a parallelogram PQRS taken in order are P ( 3 , 4 ) , Q ( − 2 , 3 ) and R ( − 3 , − 2 ), then the coordinates of its fourth vertex S are a. ( − 2 , − 1 ) b. ( − 2 − 3 ) c ( 2 − 1 ) d. ( 1 , 2 ) Sol. Let coordinates of fourth vertex of a parallelogram are 5 ( x , y ) So. option (d) is correct. Q 2 5. If the vertices of a parallelogram PQRS taken in order are P ( 3 , 4 ) , Q ( − 2 , 3 ) and R ( − 3 , − 2 ), then the coordinates of its fourth vertex S are a. ( − 2 , − 1 ) b. ( − 2 − 3 ) c ( 2 − 1 ) d. ( 1 , 2 ) Sol. Let coordinates of fourth vertex of a parallelogram are 5 ( x , y ) Updated On Jan 16, 2023 Topic All topics Subject Mathematics Class Class 11 Answer Type Video solution: 1 Upvotes 143 Avg. Video Duration 4 min

Important Important Important Important You are here Important Important Important Important Important Important Important Important Important Important Important Important Important Important Important Important Important Important Important Important Important Important Important Important Important

It is given that P(2, 4), Q(0, 3), R(3, 6) and S(5, y) are the vertices of a parallelogram PQRS. Join PR and QS, intersecting each other at O. We know that the diagonals of the parallelogram bisect each other. So, O is the mid-point of PR and QS. Coordinates of mid-point of PR = \[\left( \frac = 5\] \[ \Rightarrow 3 + y = 10\] \[ \Rightarrow y = 7\] Thus, the value of yis 7.