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Question
Divide a line segment of length 14 cm internally in the ratio 2 : 5. Also, justify your construction.
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Solution
Given that
Determine a point which divides a line segment of length
internally in the ratio of
.
We follow the following steps to construct the given
Step of construction
Step: I-First of all we draw a line segment
.
Step: II- We draw a ray 
making an acute angle
with
.
Step: III- Draw a ray 
parallel to AX by making an acute angle
.
Step IV- Mark of two points 
on and three points 
on in such a way that
.
Step: V- Joins 
and this line intersects at a point P.
Thus, P is the point dividing internally in the ratio of
Justification:
In 
we have
And 
So, AA similarity criterion, we have
Given that
Determine a point which divides a line segment of lengthinternally in the ratio of.
We follow the following steps to construct the given
Step of construction
Step: I-First of all we draw a line segment.
Step: II- We draw a ray making an acute anglewith.
Step: III- Draw a ray parallel to AX by making an acute angle.
Step IV- Mark of two points on and three points on in such a way that.
Step: V- Joins and this line intersects at a point P.
Thus, P is the point dividing internally in the ratio of
Justification:
In we have
And
So, AA similarity criterion, we have
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