# CBSE Class 10-Mathematics: Chapter – 7 Coordinate Geometry Part 11 (For CBSE, ICSE, IAS, NET, NRA 2023)

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**Question 3**:

Find the centroid of the triangle whose vertices are and .

**Answer**:

Let be the coordinate of centroid

Coordinate of centroid is

**Question 4**:

Prove that in a right-angled triangle, the mid-point of the hypotenuse is equidistant from the vertices.

**Answer**:

Let are the vertices of right-angled triangle

Coordinate of

i.e..

Hence, is Equidistant from the vertices.

**Question 5**:

Prove that diagonals of a rectangle bisect each other and are equal.

**Answer**:

Let ABCD be a rectangle take A as origin the vertices of a rectangle are

Mid-point of

Mid-point of

Mid-point of Mid-point of

Hence proved

**Question 6**:

The line joining the points is bisected at P. If P lies on the line find the value of .

**Answer**:

Coordinate of

P lies on equation