Q21 of 180 Page 3

Calculate the perimeter of a triangle with vertices (0, 4), (0, 0) and (3, 0) is

OR


The point which divides the line segment joining the points (7, - 6) and (3, 4) in ratio 1:2 internally lies in which quadrant?



We plot the vertices of a triangle i.e., (0, 4), (0, 0) and (3, 0) on the paper shown as given below



Now, perimeter of ΔAOB = Sum of the length of all its sides:



Distance between the points



= Distance between A(0, 4) and O(0, 0) + Distance between O(0, 0) and B(3, 0)


+ Distance between A(0, 4) and B(3, 0)



Hence, the required perimeter of triangle is 12.


OR


Let’s take A and B the joining point and P is the dividing point;


Let’s assume the co - ordinates of point P = x and y


By using Section formula;


x co - ordinate of point P will be -


x = and


y co - ordinate of point P will be -



؞ x =



Given that,


x1 = 7, y1 = - 6,


x2 = 3, y2 = 4


m = 1 and


n = 2




So, (x, y) = lies in IV quadrant.


[Since, in IV quadrant, x - coordinate is positive and y - coordinate is negative]


More from this chapter

All 180 →
19

In a potato race, a bucket is placed at the starting point, which is
5 m from the first potato and the other potatoes are placed 3 m apart in a straight line. There are ten potatoes in the line (as shown in figure)


A competitor starts from the bucket, picks up the nearest potato, runs back with it, drops it in the bucket, runs back to pick up the next potato, runs to the bucket to drop it in, and she continues in the same way until all the potatoes are dropped in the bucket.


(i) What is distance run to pick up the 1st potato?


(a) 8 m


(b) 10 m


(c) 12 m


(d) 9 m


(ii) What is the distance run to pick up the 2nd potato?


(a) 12 m


(b) 15 m


(c) 16 m


(d) 14 m


(iii) What is the distance run to pick up the 3rd potato?


(a) 22 m


(b) 18 m


(c) 21 m


(d) 15 m


(iv) What is the distance run to pick up the 4th potato?


(a) 26 m


(b) 30 m


(c) 25 m


(d) 28 m


(v) What is the total distance run by the competitor?


(a) 370 m


(b) 350 m


(c) 355 m


(d) 375 m


 20

An aeroplane leaves an airport and flies to north at a speed of 1000 km/hr. At the same time, another aeroplane leaves the same airport and files to west at a speed of 1200 km/hr.


(i) Find the distance covered by first plane in the north direction after 11/2 hours?


(a) 1500 km


(b) 1600 km


(c) 1400 km


(d) 1300 km


(ii) Find the distance covered by second plane in the west direction after 11/2 hours


(a) 1700 km


(b) 1800 km


(c) 1900 km


(d) 2000 km


(iii) How far apart will be the two planes after 11/2 hours?


(a) 300 59 km


(b) 300 63 km


(c) 300 61 km


(d) 300 65 km


(iv) The triangle having an angle of measure 90° is called .............. angle triangle.


(a) Right


(b) obtuse


(c) acute


(d) None of these


(v) If a line is drawn parallel to one side of a triangle to intersect the other two sides indistinct points; the other two sides are divided in the same ratio. This theorem is known as:


(a) Basic Proportionality


(b) Converse of Thales theorem


(c) Pythagoras theorem


(d) Similarity of triangles


 22

If ∆ABC~∆QRP, AB = 18cm and BC = 15cm, then what is the length of PR?

 23

If radii of two concentric circles are 4 cm and 5 cm, then find the length of each chord of one circle which is tangent to the other circle.