# CBSE Class 10-Mathematics: Chapter –7 Coordinate Geometry Part 14

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**Question 16:**

To conduct sports day activities, in your rectangular shaped school ground ABCD, lines have been drawn with chalk powder at a distance of 1 m each. 100 flowerpots have been placed at a distance of 1 m from each other along AD. Niharika runs 14th of the distance AD on the 2nd line and posts a green flag. Preet runs 15^{th} of the distance AD on the eighth line and posts a red flag. What is the distance between both the flags? If Rashmi has to post a blue flag exactly halfway between the line segment joining the two flags, where should she post her flag?

**Answer:**

Niharika runs 14^{th} of the distance AD on the 2^{nd} line and posts a green flag.

There are flowerpots. It means, she stops at 25^{th} flowerpot.

Therefore, the coordinates of point where she stops are .

Preet runs 15^{th} of the distance AD on the eighth line and posts a red flag. There are flowerpots. It means, she stops at 20^{th} flowerpot.

Therefore, the coordinates of point where she stops are .

Using Distance Formula to find distance between points and , we get

Rashmi posts a blue flag exactly halfway the line segment joining the two flags.

Using section formula to find the coordinates of this point, we get

Therefore, coordinates of point, where Rashmi posts her flag are .

It means she posts her flag in 5^{th} line after covering of distance

**Question 17:**

If A and B are and respectively, find the coordinates of P such that and P lies on the line segment AB.

**Answer:**

and

It is given that

So, we have

Let coordinates of P be

Using Section formula to find coordinates of P, we get

Therefore, Coordinates of point P are .

**Question 18:**

In each of the following find the value of ‘k’, for which the points are collinear.

(i)

(ii)

**Answer:**

(i)

Since, the given points are collinear, it means the area of triangle formed by them is equal to zero.

Area of Triangle

(ii)

Since, the given points are collinear, it means the area of triangle formed by them is equal to zero.

Area of Triangle