# CBSE Class 10-Mathematics: Chapter – 7 Coordinate Geometry Part 13 (For CBSE, ICSE, IAS, NET, NRA 2023)

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**Question 12**:

Show that the points and are the vertices of a square.

**Answer**:

Diagonal

Diagonal

Hence proved.

**Question 13**:

If the point is equidistant from the points and , prove that

**Answer**:

**Question 14**:

Find the point on the x – axis which is equidistant from and .

**Answer**:

Let the point be (x, 0) on x – axis which is equidistant from and .

Using Distance Formula and according to given conditions we have:

Therefore, point on the x – axis which is equidistant from and is

**Question 15**:

Find the coordinates of the points of trisection of the line segment joining and .

**Answer**:

We want to find coordinates of the points of trisection of the line segment joining and

We are given

We want to find coordinates of point C and D.

Let coordinates of point C be and let coordinates of point D be .

Clearly, point C divides line segment AB in and point D divides line segment AB in .

Using Section Formula to find coordinates of point C which divides join of and in the ratio , we get

Therefore, coordinates of point are and coordinates of point D are