If the length of simple pendulum is increased by 44% then what is the change in the time period of the pendulum? (a) 22 % (b) 20 % (c) 33 % (d) 44 %

The equation of line joining (x1,y1) and (x2,y2) is y−y1y2−y1=x−x1x2−x1

Hence equation of line joining (1,3) and (2,7) is

y−37−3=x−12−1 or y−34=x−11

i.e. 4x−4=y−3 or y=4x−1

Solution of equations 3x+y=9 and y=4x−1 gives point of intersection. Putting second equation in first we get

3x+4x−1=9 or x=107 and y=4×107−1=337

i.e. point of intersection is (107,337)

Now distance of (107,337) and (1,3) is

√(107−1)2+(337−3)2=√949+14449=√1537

and distance of (107,337) and (2,7) is

√(107−2)2+(337−7)2=√1649+25649=√2727

and ratio is √153√272=√17×3×3√17×4×4=34

Hence, the line joining the points (1,3) and (2,7) is divided by the line 3x+y=9 in the ratio of 3:4.

The equation of line joining (x1,y1) and (x2,y2) is y−y1y2−y1=x−x1x2−x1

Hence equation of line joining (1,3) and (2,7) is

y−37−3=x−12−1 or y−34=x−11

i.e. 4x−4=y−3 or y=4x−1

Solution of equations 3x+y=9 and y=4x−1 gives point of intersection. Putting second equation in first we get

3x+4x−1=9 or x=107 and y=4×107−1=337

i.e. point of intersection is (107,337)

Now distance of (107,337) and (1,3) is

√(107−1)2+(337−3)2=√949+14449=√1537

and distance of (107,337) and (2,7) is

√(107−2)2+(337−7)2=√1649+25649=√2727

and ratio is √153√272=√17×3×3√17×4×4=34

Hence, the line joining the points (1,3) and (2,7) is divided by the line 3x+y=9 in the ratio of 3:4.