To divide a line segment AB in the ratio 5:7, first AX is drawn, so that angle BAX is an acute angle and then at equal distance , points are marked on the ray AX, find the maximum number of these points
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The maximum number of points = 5+7 = 12
In this process, once line AX is drawn, it is divided into 12 equal parts using a pair of compasses.
The points are marked from point A towards X. The last point is then joined to point B to form line XB.
Lines are then drawn parallel to XB and passing through the points that were marked on AX. These lines can be drawn using set squares to ensure they are parallel.
These parallel lines will divide line AB into 12 equal parts. So, to divide the line in the ratio 5:7, the first five portions will be taken and the last 7 left as shown in the attached figure.
In this process, once line AX is drawn, it is divided into 12 equal parts using a pair of compasses.
The points are marked from point A towards X. The last point is then joined to point B to form line XB.
Lines are then drawn parallel to XB and passing through the points that were marked on AX. These lines can be drawn using set squares to ensure they are parallel.
These parallel lines will divide line AB into 12 equal parts. So, to divide the line in the ratio 5:7, the first five portions will be taken and the last 7 left as shown in the attached figure.
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We know that to divide a line segment AB in the ratio m:n we have to follow the following steps of construction:
1.Draw a line segment AB of a given length by using a ruler.
2. Draw any Ray AX making an acute angle with AB.
3. Along AX mark off (m+n) points A1,A2,A3,….Am , A(m+1), A(m+n) such that AA1= AA2= A(m+n-1)A(m+n).
4.Join BA(m+n).
5. Through the point Am draw a line parallel to A(m+n) by making an angle equal to ∠AA(m+n) which intersects the line segment AB at point P.
The point P so obtained is the required point which divides AB internally in the ratio m:n.
Here, m= 5 , n= 7
Hence,the maximum number of points on the ray AX = 5+7= 12.
HOPE THIS WILL HELP YOU...
1.Draw a line segment AB of a given length by using a ruler.
2. Draw any Ray AX making an acute angle with AB.
3. Along AX mark off (m+n) points A1,A2,A3,….Am , A(m+1), A(m+n) such that AA1= AA2= A(m+n-1)A(m+n).
4.Join BA(m+n).
5. Through the point Am draw a line parallel to A(m+n) by making an angle equal to ∠AA(m+n) which intersects the line segment AB at point P.
The point P so obtained is the required point which divides AB internally in the ratio m:n.
Here, m= 5 , n= 7
Hence,the maximum number of points on the ray AX = 5+7= 12.
HOPE THIS WILL HELP YOU...
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